Fiber Bragg Gratings

Fiber Bragg Gratings

Fiber Bragg Gratings

OPTICS AND PHOTONICS (formerly Quantum Electronics) E D I T E D BY

PAUL L. KELLY Tufts University Medford, Massachusetts

IVAN KAMINOW Lucent Technologies Holmdel, New Jersey

GOVIND AGRAWAL University of Rochester Rochester, New York

A complete list of titles in this series appears at the end of this volume.

Fiber Bragg Gratings Raman Kashyap

BT Laboratories, Martlesham Heath

Ipswich, United Kingdom

ACADEMIC PRESS San Diego London Boston New York Sydney Tokyo Toronto

The cover picture shows the near-field photographs of radiation mode patterns of several low-order counterpropagating modes (LP0n). These are excited by the forward propagating core mode in a 6-mm-long, side-tap grating with a 2 ~ blaze angle, written into the core of a single mode fiber. Artwork by Arjun Kashyap.

This book is printed on acid-free paper. Copyright 9 1999 by Academic Press All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. ACADEMIC PRESS a division of Harcourt Brace & Company 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA http://www.apnet.com ACADEMIC PRESS 24-28 Oval Road, London, NWl 7DX, UK http://www.hbuk.co.uk/ao/

Library of Congress Catalog Card Number: 99-60954 International Standard Book Number: 0-12-400560-8

Printed in the United States of America 99 00 01 02 03 IP 9 8 7 6 5

4

3

2

1

For Monika, Hannah, and in memory of Prof. Kedar Nath Kashyap

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Contents Preface

xiii

Chapter 1 Introduction 1.1 Historical perspective 1.2 Materials for glass fibers 1.3 Origins of the refractive index of glass 1.4 Overview of chapters References

1 2 4 6 8 10

Chapter 2

2.1 2.2 2.3 2.4

2.5 2.6 2.7

Photosensitivity and Photosensitization of Optical Fibers Photorefractivity and photosensitivity Defects in glass Detection of defects Photosensitization techniques 2.4.1 Germanium-doped silica fibers 2.4.2 Germanium-boron codoped silicate fibers 2.4.3 Tin-germanium codoped fibers 2.4.4 Cold, high-pressure hydrogenation 2.4.5 Rare-earth-doped fibers Densification and stress in fibers Summary of photosensitive mechanisms in germanosilicate fibers Summary of routes to photosentization 2.7.1 Summary of optically induced effects References

Chapter 3 Fabrication of Bragg Gratings 3.1 Methods for fiber Bragg grating fabrication

vii

13 14 16 19 20 21 27 29 29 34 35 36 38 42 44 55 55

viii

Contents

3.1.1 3.1.2 3.1.3 3.1.4 3.1.5 3.1.6 3.1.7 3.1.8 3.1.9 3.1.10 3.1.11 3.1.12 3.1.13

3.2 3.3 3.4

The bulk interferometer The phase mask The phase mask interferometer Slanted grating The scanned phase mask interferometer The Lloyd mirror and prism interferometer Higher spatial order masks Point-by-point writing Gratings for mode and polarization conversion Single-shot writing of gratings Long-period grating fabrication Ultralong-fiber gratings Tuning of the Bragg wavelength, moir6, Fabry-Perot, and superstructure gratings 3.1.14 Fabrication of continuously chirped gratings 3.1.15 Fabrication of step-chirped gratings Type II gratings Type IIA gratings Sources for holographic writing of gratings 3.4.1 Low coherence sources 3.4.2 High coherence sources References

Chapter 4 Theory of Fiber Bragg Gratings 4.1 Wave Propagation 4.1.1 Waveguides 4.2 Coupled-mode theory 4.2.1 Spatially periodic refractive index modulation 4.2.2 Phase matching 4.2.3 Mode symmetry and the overlap integral 4.2.4 Spatially periodic nonsinusoidal refractive index modulation 4.2.5 Types of mode coupling 4.3 Coupling of counterpropagating guided modes 4.4 Codirectional coupling 4.5 Polarization couplers: Rocking filters 4.6 Properties of uniform Bragg gratings 4.6.1 Phase and group delay of uniform period gratings

55 57 62 69 71 74 77 80 80 83 84 85 88 93 99 101 101 102 102 104 108 119 121 122 125 127 130 131

133 134 142 145 148 152 155

Contents

4.7

4.8

4.9

Radiation mode couplers 4.7.1 Counterpropagating radiation mode coupler: The side-tap grating 4.7.2 Copropagating radiation mode coupling: Longperiod gratings Grating simulation 4.8.1 Methods for simulating gratings 4.8.2 Transfer matrix method Multilayer analysis 4.9.1 Rouard's method 4.9.2 The multiple thin-film stack References

ix

157 157 171 178 178 179 185 185 186 189

Chapter 5 Apodization of Fiber Gratings Apodization shading functions 5.1 5.2 Basic principles and methodology 5.2.1 Self-apodization 5.2.2 The amplitude mask 5.2.3 The variable diffraction efficiency phase mask 5.2.4 Multiple printing of in-fiber gratings applied to apodization 5.2.5 Position-weighted fabrication of top-hat reflection gratings 5.2.6 The moving fiber/phase mask technique 5.2.7 The symmetric stretch apodization method Fabrication requirements for apodization and chirp 5.3 References

195 197 199 200 203 205

Chapter 6 Fiber Grating Band-pass Filters 6.1 Distributed feedback, Fabry-Perot, superstructures, and moir~ gratings 6.1.1 The distributed feedback grating 6.1.2 Superstructure band-pass filter 6.2 The Fabry-Perot and moir~ band-pass filters 6.3 The Michelson interferometer band-pass filter 6.3.1 The asymmetric Michelson multiple-band-pass filter 6.4 The Mach-Zehnder interferometer band-pass filter

227

206 208 211 216 221 223

229 229 239 242 246 255 260

Contents

6.4.1

6.5 6.6 6.7

6.8 6.9 6.10

Optical add-drop multiplexers based on the GMZI-BPF The optical circulator based OADM 6.5.1 Reconfigurable OADM The polarizing beam splitter band-pass filter In-coupler Bragg grating filters 6.7.1 Bragg reflecting coupler OADM 6.7.2 Grating-frustrated coupler Side-tap and long-period grating band-pass filters Polarization rocking band-pass filter Mode converters 6.10.1 Guided-mode intermodal couplers References

263 265 270 272 276 278 284 288 293 297 297 300

Chapter 7 Chirped Fiber Bragg Gratings 7.1 General characteristics of chirped gratings Chirped and step-chirped gratings 7.2 7.2.1 Effect of apodization 7.2.2 Effect of nonuniform refractive index modulation on grating period 7.3 Super-step-chirped gratings Polarization mode dispersion in chirped gratings 7.4 Systems measurements with DCGs 7.5 7.5.1 Systems simulations and chirped grating performance Other applications of chirped gratings 7.6 References

311 312 317 324

Chapter 8 Fiber Grating Lasers and Amplifiers 8.1 Fiber grating semiconductor lasers: The FGSL 8.2 Static and dynamic properties of FGLs 8.2.1 Modeling of external cavity lasers 8.2.2 General comments on FGLs 8.3 The fiber Bragg grating rare-earth-doped fiber laser 8.4 Erbium-doped fiber lasers 8.4.1 Single-frequency erbium-doped fiber lasers The distributed feedback fiber laser 8.5 8.5.1 Multifrequency sources 8.5.2 Tunable single-frequency sources

355 355 362 366 369 370 372 374 377 379 380

330 332 336 339 342 346 347

Contents

8.6 8.7 8.8

Bragg grating based pulsed sources Fiber grating resonant Raman amplifiers Gain-flattening and clamping in fiber amplifiers 8.8.1 Amplifier gain equalization with fiber gratings 8.8.2 Optical gain control by gain clamping 8.8.3 Analysis of gain-controlled amplifiers 8.8.4 Cavity stability 8.8.5 Noise figure References

Chapter 9

9.1 9.2 9.3

9.4

Index

xi

380 383 385 387 391 395 396 397 398

M e a s u r e m e n t and C h a r a c t e r i z a t i o n o f Gratings

409

Measurement of reflection and transmission spectra of Bragg gratings Perfect Bragg gratings Phase and temporal response of Bragg gratings 9.3.1 Measurement of the grating profile 9.3.2 Measurement of internal stress Strength, annealing, and lifetime of gratings 9.4.1 Mechanical strength 9.4.2 Bragg grating lifetime and thermal annealing 9.4.3 Accelerated aging of gratings References

417 418 426 432 435 435 436 440 441 447

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Preface The field of fiber Bragg gratings is almost exactly twenty years old, dating back to its discovery by Ken Hill and co-workers in Canada. It grew slowly at first, but an important technological advance by Gerry Meltz and coworkers 10 years later, renewed worldwide interest in the subject. I was instrumental in setting up the first International Symposium on photosensitivity of optical fibers, jointly with Francois Ouellette in 1991, a meeting with 22 presentations and attended by approximately 50 researchers. Since, we have seen three further international conferences solely devoted to fiber Bragg gratings, the last of which was attended by approximately 300 researchers. As the applications of Bragg gratings are numerous, publications appear in widely differing conferences and journals. Surprisingly, apart from several review articles covering the most elementary aspects, no monograph is available on the subject and the quantity of available literature is spread across a number of specialist journals and proceedings of conferences. Thus, progress and the current state of the art are difficult to track, despite the approaching maturity of the field. More recently, poling of glass optical fibers has resulted in an electrooptic coefficient almost rivaling that of lithium niobate. Germanium, the core dopant of low loss, fused silica optical fiber, is a rich defect former; ultraviolet radiation can strongly modify the nature of the defects causing large changes in the local refractive index. The mechanisms contributing to photosensitivity are complicated and still being debated. They depend on the types of defects present, dopants, and the presence of hydrogen whether in the molecular or in the ionic state. The lack of a thorough understanding has not, however, prevented the exploitation of the effect in a large number of applications. The very large index changes reported to date (~0.03) allow, for the first time, the fabrication of ultra-short (~100 ~m long) broadband, high-reflectivity Bragg gratings in optical fibers. The maximum index change may be an xiii

xiv

Preface

order of magnitude larger still, leading to many more exciting possibilities. There are a number of methods of the holographic inscription of Bragg gratings, with the phase-mask technique holding a prominent position. This book was born as a result of growing demands for yet more review articles on the subject. It aims to fill the gap by bringing together the fundamentals of fiber gratings, their specific characteristics, and many of the applications. The book covers much of the fundamental material on gratings and should be of interest to beginners, advanced researchers, as well as those interested in the fabrication of many types of gratings. It is impossible to cover the massive advances made in this field in a book of this size, a field that continues to grow at an enormous rate despite recent commercialization. A large reference list is provided, to allow the interested reader to seek out specific topics in more detail. The purpose of this book is therefore to introduce the reader to the extremely rich area of the technology of fiber Bragg, with a view to providing insight into some of the exciting prospects. It begins with the principles of fiber Bragg gratings, photosensitization of optical fibers, Bragg grating fabrication, theory, properties of gratings, and specific applications, and concludes with measurement techniques.

BT Laboratories, Ipswich IP5 3RE, United Kingdom July 1998

Raman Kashyap

Acknowledgments I am grateful to many individuals who have either directly contributed to the book or so generously provided material for it. I thank the members of the European ACTS Program, PHOTOS, whose efforts have greatly contributed to the growing knowledge in this area. In particular, I am indebted to Marc Douay, Bertrand Poumellec, Ren~ Salathe, Pierre Sansonetti, Isabelle Riant, Fatima Bhakti, Hans Limberger, and Christian Bungarzaneau, for providing several original exemplary figures and simulations. I thank Ken Hill, Jacques Albert, Stanislav Chernikov, Turan Erdogan, Phillip Russell, Feodor Timofeev, Malin Permanante, Raoul Stubbe, Vince Handerek, Sotiris Kanellopoulos, Tom Strasser, Peter Krug, Takashi Mizuochi, Nadeem Rizvi, Doug Williams, Alistair Poustie, Steve Kershaw, and Mike Brierley for their assistance with figures, Arjun Kashyap for the arrangement on the front cover, and others who have also provided data for inclusion in the book. Melanie Holmes's vast contribution on radiation mode coupling is humbly acknowledged. I especially thank her for the many philosophical discussions, fun arguments and Mars bars exchanged on the subject! Jenny Massicott has generously contributed and provided significant help with the section on gain controlled amplifiers. 'Thanks' must go to Richard Wyatt for reading the manuscript so quickly and Marcello Segatto for his many constructive comments. A special thank you to Domenico Giannone for his painstaking and careful reading of parts of the manuscript, and to Hans Georg FrShlich and Simon Wolting for undertaking fun experiments during their summer student-ships. Monica de Lacerda-Rocha provided numerous measurements on chirped gratings. Walter Margulis and Isabel Cristina Carvalho are acknowledged for the amusing times in the lab in Rio, proving that writing in-fiber gratings on a piece of Amazonian hardwood "optical bench" is easy, even late at night! Bernhard Lesche and Isabel Cristina Carvalho xv

xvi

Acknowledgments

contributed to interesting discussions during the writing of the book. Martin Burley kept me amused with his music and sense of humor during the lulls in writing. The IEEE, IEE, OSA and Elsevier Science are acknowledged for provision of copyright permission on several figures. I also gratefully acknowledge D. W. Smith of BT Laboratories for his generous support and provision of computer facilities for the production of the manuscript. Finally, I am deeply appreciative of Monika and Hannah, whose unquestioning patience, support and provision of earthly comforts formed essential ingredients in the birth of this book.

Fiber Bragg Gratings

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Chapter

1

Introduction

Optical fibers have revolutionized telecommunication. Much of the success of optical fiber lies in its near-ideal properties: low transmission loss, high optical damage threshold, and low optical nonlinearity. The combination of these properties has enabled long-distance communication to become a reality. At the same time, the long lengths enabled the optical power to interact with the small nonlinearity to give rise to the phenomenon of optical solitons, overcoming the limit imposed by linear dispersion. The market for optical fiber continues to grow, despite the fact t h a t major trunk routes and metropolitan areas have already seen a large deployment of fiber. The next stage in the field of communication is the mass delivery of integrated services, such as home banking, shopping, Internet services, and e n t e r t a i n m e n t using video-on-demand. Although the bandwidth available on single mode fiber should meet the ever-increasing demand for information capacity, architectures for future networks need to exploit technologies which have the potential of driving down cost to make services economically viable. Optical fiber will have to compete with other transport media such as radio, copper cable, and satellite. Short-term economics and long-term evolutionary potential will determine the type of technology likely to succeed in the provision of these services. But it is clear t h a t optical fibers will play a crucial role in communication systems of the future. The technological advances made in the field of photosensitive optical fibers are relatively recent; however, an increasing number of fiber devices based on this technology are getting nearer to the m a r k e t place. It is believed t h a t they will provide options to the network designer that should influence, for example, the deployment of wavelength-divi-

2

Chapter i

Introduction

sion-multiplexed (WDM) systems, channel selection, and deployment of t r a n s m i t t e r s in the u p s t r e a m path in a network, and should make routing viable. The fascinating technology of photosensitive fiber is based on the principle of a simple in-line all-fiber optical filter, with a vast number of applications to its credit.

1.1

Historical perspective

Photosensitivity of optical fiber was discovered at the Canadian Communication Research Center in 1978 by Ken Hill et al. [1] during experiments using germania-doped silica fiber and visible argon ion laser radiation. It was noted t h a t as a function of time, light launched into the fiber was increasingly reflected. This was recognized to be due to a refractive index grating written into the core of the optical fiber as a result of a standing wave intensity pattern formed by the 4% back reflection from the far end of the fiber and forward-propagating light. The refractive index grating grew in concert with the increase in reflection, which in turn increased the intensity of the standing wave pattern. The periodic refractive index variation in a meter or so of fiber was a Bragg grating with a bandwidth of around 200 MHz. But the importance of the discovery in future applications was recognized even at t h a t time. This curious phenomenon remained the preserve of a few researchers for nearly a decade [2,3]. The primary reason for this is believed to be the difficulty in setting up the original experiments, and also because it was thought t h a t the observations were confined to the one "magic" fiber at CRC. Further, the writing wavelength determined the spectral region of the reflection grating, limited to the visible part of the spectrum. Researchers were already experimenting and studying the even more bizarre phenomenon of second-harmonic generation in optical fibers made of germania-doped silica, a material t h a t has a zero second-order nonlinear coefficient responsible for second-harmonic generation. The observation was quite distinct from another nonlinear phenomenon of sumfrequency generation reported earlier by Ohmori and Sasaki [4] and Hill et al. [5], which were also curious. Ulf Osterberg and Walter Margulis [6] found t h a t ML-QS infrared radiation could "condition" a germania dopedsilica fiber after long exposure such t h a t second-harmonic radiation grew (as did Ken Hill's reflection grating) to nearly 5% efficiency and was soon identified to be a grating formed by a nonlinear process [7,8]. Julian

1.1

Historical perspective

3

Stone's [9] observation that virtually any germania-doped silica fiber demonstrated a sensitivity to argon laser radiation reopened activity in the field of fiber gratings [10,11] and for determining possible links between the two photosensitive effects. Bures et al. [12] had pointed out the twophoton absorption nature of the phenomenon from the fundamental radiation at 488 nm. The major breakthrough came with the report on holographic writing of gratings using single-photon absorption at 244 nm by Gerry Meltz et al. [13]. They demonstrated reflection gratings in the visible part of the spectrum (571-600 nm) using two interfering beams external to the fiber. The scheme provided the much-needed degree of freedom to shift the Bragg condition to longer and more useful wavelengths, predominantly dependent on the angle between the interfering beams. This principle was extended to fabricate reflection gratings at 1530 nm, a wavelength of interest in telecommunications, also allowing the demonstration of the first fiber laser operating from the reflection of the photosensitive fiber grating [14]. The UV-induced index change in untreated optical fibers was ~10 -4. Since then, several developments have taken place that have pushed the index change in optical fibers up a hundredfold, making it possible to create efficient reflectors only a hundred wavelengths long. Lemaire and coworkers [15] showed that the loading of optical fiber with molecular hydrogen photosensitized even standard telecommunication fiber to the extent that gratings with very large refractive index modulation could be written. Pure fused silica has shown yet another facet of its curious properties. It was reported by Brueck et al. [16] that at 350~ a voltage of about 5 kV applied across a sheet of silica, a millimeter thick, for 30 minutes resulted in a permanently induced second-order nonlinearity of ~1 pm/V. Although poling of optical fibers had been reported earlier using electric fields and blue-light and UV radiation [17-19], Wong et al. [20] demonstrated that poling a fiber while writing a grating with UV light resulted in an enhanced electro-optic coefficient. The strength of the UV-written grating could be subsequently modulated by the application of an electric field. More recently, Fujiwara et al. reported a similar photoassisted poling of bulk germanium-doped silica glass [21]. The silica-germanium system will no doubt produce further surprises. All these photosensitive processes are linked in some ways but can also differ dramatically in their microscopic detail. The physics of the effect continues to be debated, although the presence of defects plays a

Chapter 1 Introduction central role in more t h a n one way. The field r e m a i n s an active area for research.

1.2

Materials

for glass fibers

Optical fiber for communications has evolved from early predictions of lowest loss in the region of a few decibels per kilometer to a final achieved value of only 0.2 dB km-1. The reason for the low optical loss is several fortuitous m a t e r i a l properties. The b a n d g a p of fused silica lies at around 9 eV [22], while the infrared vibrational resonances produce an edge at a w a v e l e n g t h of a r o u n d 2 microns. Rayleigh scatter is the d o m i n a n t loss m e c h a n i s m with its characteristic ~-4 dependence in glass fibers indicating a n e a r perfect homogeneity of the m a t e r i a l [23]. The refractive index profile of an optical fiber is shown in Fig. 1.1. The core region h a s a higher refractive index t h a n the s u r r o u n d i n g cladding material, which is usually m a d e of silica. Light is therefore t r a p p e d in the core by total internal reflection at the core-cladding boundaries and is able to travel tens of kilometers with little a t t e n u a t i o n in the 1550-nm w a v e l e n g t h region. One

Core Cladding Refractive Index I

-a

+a

i

Silica AIR

-r

Figure

+r

1.1: Cross-section of an optical fiber with the corresponding refractive index profile. Typically, the core-to-cladding refractive index difference for singlemode telecommunications fiber at a wavelength of 1.5 ttm is -4.5 x 10 -3 with a core radius of 4 ttm.

1.2 Materials for glass fibers

5

of the commonly used core dopants, germanium, belongs to Group IVA, as does silicon and replaces the silicon atom within the tetrahedron, coordinated with four oxygen atoms. Pure germania has a band edge at around 185 nm [24]. Apart from these pure material contributions, which constitute a fundamental limit to the attenuation characteristics of the waveguide, there may be significant absorption loss from the presence of impurities. The O H - ion has IR absorptions at wavelengths of 1.37, 0.95, and 0.725 ttm [25], overtones of a stretching-mode vibration at a fundamental wavelength of 2.27 ttm. Defect states within the ultraviolet and visible wavelength band of 190-600 nm [26] also contribute to increased absorption. The properties of some of these defects will be discussed in Chapter 2. The presence of phosphorus as P205 in silica, even in small quantities (-0.1%), reduces the glass melting point considerably, allowing easier fabrication of the fiber. Phosphorus is also used in fibers doped with rare earth compounds such as Yb and Er for fiber amplifiers and lasers. In high concentration rare earth ions tend to cluster in germanium-doped silicate glasses. Clustering causes ion-ion interaction, which reduces the excited state lifetimes [27]. Along with aluminum (A1203 as a codopant in silica) in the core, clustering is greatly reduced, enabling efficient amplifiers to be built. Phosphorus is also commonly used in planar silica on silicon waveguide fabrication, since the reduced processing temperature reduces the deformation of the substrate [28]. Fluorine and trivalent boron (as B203) are other dopants commonly used in germania-doped silica fiber. A major difference between germanium and fluorine/boron is that while the refractive index increases with increasing concentration of germanium, it decreases with boron/fluorine. With fluorine, only modest reductions in the refractive index are possible (-0.1%), whereas with boron large index reductions (>0.02) are possible. Boron also changes the topology of the glass, being trivalent. Boron and germanium together allow a low refractive index difference between the core and cladding to be maintained with large concentrations of both elements [29]. On the other hand, a depressed cladding fiber can be fabricated by incorporating boron in the cladding to substantially reduce the refractive index. The density of the boron-doped glass may be altered considerably by annealing, by thermally cycling the glass, or by changing the fiber drawing temperature [30]. Boron-doped preforms exhibit high stress and shatter easily unless handled with care. The thermal history changes the density

6

Chapter i

Introduction

and stress in the glass, thereby altering the refractive index. The thermal expansion of boron-silica glass is - 4 x 10-6~ -1, several times that of silica (7 • 10-7~ -1) [31]. Boron-doped silica glass is generally free of defects, with a much reduced melting temperature. Boron being a lighter atom, the vibrational contribution to the absorption loss extends deeper into the short wavelength region and increases the absorption loss in the 1500-nm window. Boron with g e r m a n i u m doping has been shown to be excellent for photosensitivity [29].

1.3

Origins of the refractive

index of glass

The refractive index n of a dielectric may be expressed as the summation of the contribution of i oscillators of strength f/each, as [32] n2-

1_4r

n 2 -4- 2

e2 ~ 3 m s o ~ii a ~ i -

f/ w2 + iFiw'

(1.1.1)

where e and m are the charge and mass of the electron, respectively, w i is the resonance frequency, and F i is a damping constant of the ith oscillator. Therefore, refractive index is a complex quantity, in which the real part contributes to the phase velocity of light (the propagation constant), while the sign of the imaginary part gives rise to either loss or gain. In silica optical fibers, far away from the resonances of the deep UV wavelength region, which contribute to the background refractive index, the loss is negligible at telecommunications wavelengths. However, the presence of defects or rare-earth ions can increase the absorption, even within in the transmission windows of 1.3 to 1.6 microns in silica optical fiber. F i can be neglected in low-loss optical fibers in the telecommunications transmission band, so that the real part, the refractive index, is [32] Ai,t 2 n 2 = 1 + Z ]12_ ]12" i

(1.1.2)

With i = 3, we arrive at the well-known Sellmeier expression for the refractive index, and for silica (and pure germania), the ~Ii (i = 1 ~ 3) are the electronic resonances at 0.0684043 (0.0690) and 0.1162414 (0.1540) t~m, and lattice vibration at 9.896161 (11.8419) ttm. Their strengths A i have been experimentally found to be 0.6961663 (0.8069),

1.3

Origins of the refractive index of glass

7

0.4079426 (0.7182), and 0.8974794 (0.8542) [33,34], where the d a t a in parentheses refers to GeO2. The group index N is defined as dn N = n - ~ ~--~,

(1.1.3)

which determines the velocity at which a pulse travels in a fiber. These quantities are plotted in Fig. 1.2, calculated from Eqs. (1.1.2) and (1.1.3). We note t h a t the refractive index of pure silica at 244 n m at 20~ is 1.51086. The data for germania-doped silica m a y be found by interpolation of the data for the molar concentration of both materials. Although this applies to the equilibrium state in bulk samples, they m a y be modified by the fiber fabrication process. The change in the refractive index of the fiber at a wavelength A m a y be calculated from the observed changes in the absorption spectrum in the ultraviolet using the K r a m e r s - K r o n i g relationship [32,35], An(A)

1 ~, f~l (A~i(~') . : ,,~2)d~', "7 ~ ~ ~' 2)

(2~)2

( 1.1.4)

where the summation is over discrete wavelength intervals around each of the i changes in m e a s u r e d absorption, ai. Therefore, a source of photoinduced change in the absorption at A1 -< A' -/~2 will change the refractive index at wavelength/l.

X

-o

1.6 t ",", Group 1.58 'L 1.56 \\ 1.54

Index

1.52 1.5 1.48 1.46

....

1.44 0.2

0.7

1.2

1.7

Wavelength, microns

Figure

1.2: Refractive index n and the group index, N of pure silica at 20~

8

Chapter i

Introduction

The refractive index of glass depends on the density of the material, so that a change in the volume through thermally induced relaxation of the glass will lead to a change An in the refractive index n as An n

~

AV V

~

3n 2

s,

(1.1.5)

where the volumetric change AV as a fraction of the original volume V is proportional to the fractional change ~ in linear dimension of the glass. We now have the fundamental components that may be used to relate changes in the glass to the refractive index after exposure to UV radiation. Other interesting data on fused silica is its softening point at 2273~ and the fact that it probably has the largest elastic limit of any material, - 1 7 % , at liquid nitrogen temperatures [36].

1.4

Overview

of chapters

The book begins with a simple introduction to the photorefractive effect as a comparison with photosensitive optical fibers in Chapter 2. The interest in electro-optic poled glasses is fueled from two directions: an interest in the physics of the phenomenon and its connection with photosensitive Bragg gratings, and as the practical need for devices that overcome many of the fabrication problems associated with crystalline electro-optic materials, of cutting, polishing, and in-out coupling. A fibercompatible device is an ideal, which is unlikely to be abandoned. The fiber Bragg grating goes a long way in t h a t direction. However interesting the subject of poled glasses and second-harmonic generation in glass optical fibers and nonlinear behavior of gratings, they are left for another time. With this connection left for the moment, we simply point to the defects, which are found to be in common with the process of harmonic generation, poling of glass, and Bragg gratings. The subject of defects alone is a vast spectroscopic minefield. Some of the prominent defects generally found in germania-doped fused silica that have a bearing on Bragg grating formation are touched upon. The nature and detection of the defects are introduced. This is followed by the process of photosensitizing optical fibers, including reduced germania, boron-germanium codoped fibers, Sn doping, and hydrogen loading. The different techniques and routes used to enhance the sensitivity of optical fibers,

1.4

Overview of chapters

9

including that of rare-earth doped fibers are compared in a summary at the end of Chapter 2. Chapter 3 is on fabrication of Bragg gratings. It deals with the principles of holographic, point-by-point replication and the technologies involved in the process: various arrangements of the Lloyd and mirror interferometers, phase-mask, along with the fabrication of different type of Bragg and long-period gratings, chirped gratings, and ultralong gratings. The attributes of some of the laser sources commonly used for fabrication are introduced in the concluding section of the chapter. Chapter 4 begins with wave propagation in optical fibers, from the polarization response of a dielectric to coupled mode theory, and formulates the basic equations for calculating the response of uniform gratings. A section follows on the side-tap gratings, which have special applications as lossy filters. Antenna theory is used to arrive at a good approximation to the filter response for the design of optical filters. Long-period gratings and their design follow, as well as the physics of rocking filters. The last section deals with grating simulation. Here two methods for the simulation of gratings of arbitrary profile and chirp based on the transfermatrix approach and Rouard's method of thin films are described. Chapter 5 looks in detail at the different methods available for apodization of Bragg gratings and its effect on the transfer characteristics. These include the use of the phase mask, double exposure, stretching methods, moir~ gratings, and novel schemes that use the coherence properties of lasers to self-apodize gratings. Chapter 6 introduces the very large area of band-pass filtering to correct for the "errant" property of the Bragg grating: as the band-stop filter! We begin with the distributed-feedback (DFB) structure as the simplest transmission Bragg grating, followed by the multisection grating design for the multiple band-pass function, chirped grating DFB bandpass filters widening the gap to address the Fabry-Perot structure, and moving on to the superstructure grating. Other schemes include the Michelson-interferometer-based filter, Mach-Zehnder interferometer, properties, tolerances requirements for fabrication, and a new device based on the highly detuned interferometer, which allows multiple band-pass filters to be formed, using chirped and unchirped gratings. An important area in applications is the optical add-drop multiplexer (OADM), and different configurations of these are considered, along with their advantages and disadvantages. The special filter based on the in-coupler Bragg grating as a family of filters is presented. Simple equations are suggested

10

Chapter I Introduction

for simulating the response of the Bragg reflection coupler. Rocking and mode-converting filters are also presented, along with the side-tap radiation mode and long period grating filter, as band-pass elements. Chirped gratings have found a niche as dispersion compensators. Therefore, Chapter 7 is devoted to the application of chirped gratings, with a detailed look at the dispersive properties related to apodization and imperfect fabrication conditions on the group delay and reflectivity of gratings. Further, the effect of stitching is considered for the fabrication of long gratings, and the effect of cascading gratings is considered for systems applications. Systems simulations are used to predict the biterror-rate performance of both apodized and unapodized gratings. Transmission results are also briefly reviewed. The applications of gratings in semiconductor and fiber lasers can be found in Chapter 8. Here configurations of the external cavity fiber Bragg grating laser and applications in fiber lasers as single and multiple frequency and -wavelength sources are shown. Gain flattening and clamping of erbium amplifiers is another important area for long-haul high-bit-rate and analog transmission systems. Finally, the interesting and unique application of the fiber Bragg grating as a R a m a n oscillator is shown. The ninth and final chapter deals with measurements and testing of Bragg gratings. This includes basic measurements, properties of different types of gratings, and m e a s u r e m e n t parameters. Life testing and reliability aspects of Bragg gratings conclude the book.

References 1 Hill K. O., Fujii Y., Johnson D. C., and Kawasaki B. S. "Photosensitivity in optical waveguides: Application to reflection filter fabrication," Appl. Phys. Lett. 32(10), 647 (1978). 2 Bures J., Lapiere J., and Pascale D., "Photosensitivity effect in optical fibres: A model for the growth of an interference filter," Appl. Phys. Let. 37(10), 860 (1980). 3 Lam D. W. K. and Garside B. K., "Characterisation of single-mode optical fibre filters," Appl. Opt. 20(3), 440 (1981). 4 0 h m o r i Y. and Sasaki Y., "Phase matched sum frequency generation in optical fibers," Appl. Phys. Lett. 39, 466-468 (1981). 5 Fujii Y., Kawasaki B. S., Hill K. O., and Johnson D. C., "Sum frequency generation in optical fibers," Opt. Lett. 5, 48-50 (1980).

References

11

6 Osterberg U. and Margulis W., "Efficient second harmonic in an optical fiber," in Technical Digest of X/V Internat. Quantum Electron. Conf., paper WBB1 (1986). 7 Stolen R. H. and Tom H. W. K., "Self-organized phase-matched harmonic generation in optical fibers," Opt. Lett. 12, 585-587 (1987). 8 Farries M. C., Russell P. St. J., Fermann M. E., and Payne D.N., "Second harmonic generation in an optical fiber by self-written ~2) grating," Electron. Lett. 23, 322-323 (1987). 9 Stone J., "Photorefractivity in GeO2-doped silica fibres," J. Appl. Phys. 62(11), 4371 (1987). 10 Kashyap R., "Photo induced enhancement of second harmonic generation in optical fibers," Topical Meeting on Nonlinear Guided Wave Phenomenon: Physics and Applications, 1989, Technical Digest Series, Vol. 2, held on February 2-4, 1989, Houston (Optical Society of America, Washington, D.C. 1989), pp. 255-258. 11 Hand D. P. and Russell P. St. J., "Single mode fibre gratings written into a Sagnac loop using photosensitive fibre: transmission filters," IOOC, Technical Digest, pp. 21C3-4, Japan (1989). 12 Bures J., Lacroix S., and Lapiere J., "Bragg reflector induced by photosensitivity in an optical fibre: model of growth and frequency response," Appl. Opt. 21(19) 3052 (1982). 13 Meltz G., Morey W. W., and Glenn W. H., "Formation of Bragg gratings in optical fibres by transverse holographic method," Opt. Lett. 14(15), 823 (1989). 14 Kashyap R., Armitage J. R., Wyatt R., Davey S. T., and Williams D. L., "Allfibre narrowband reflection gratings at 1500 nm," Electron. Lett. 26(11), 730 (1990). 15 Lemaire P., Atkins R. M., Mizrahi V., and Reed W.A., "High pressure H 2 loading as a technique for achieving ultrahigh UV photosensitivity and thermal sensitivity in GeO2 doped optical fibres," Electron. Lett. 29(13), 1191 (1993). 16 Myers R. A., Mukherjee N., and Brueck S. R. J., "Large second order nonlinearity in poled fused silica," Opt. Lett. 16, 1732-1734 (1991). 17 Bergot M. V., Farries M. C., Fermann M. E., Li L., Poyntz-Wright L. J., Russell P. St. J., and Smithson A., Opt. Lett. 13, 592-594 (1988). 18 Kashyap R., "Phase-matched second-harmonic generation in periodically poled optical fibers," Appl. Phys. Lett. 58(12), 1233, 25 March 1991. 19 Kashyap R., Borgonjen E., and Campbell R. J., "Continuous wave seeded second-harmonic generation optical fibres: The enigma of second harmonic generation," Proc. SPIE 2044, pp. 202-212 (1993).

12

Chapter I

Introduction

20 Fujiwara T., Wong D., and Fleming S., "Large electro-optic modulation in a thermally poled germanosilicate fiber," IEEE Photon. Technol. Lett. 7(10), 1177-1179 (1995). 21 Fujiwara T., Takahashi M., and Ikushima A. J., "Second harmonic generation in germanosilicate glass poled with ArF laser irradiation," Appl. Phys. Lett. 71(8), 1032-1034 (1997). 22 Philipp H. R., "Silicon dioxide (SiO 2) glass," in Handbook of Optical Constants of Solids (E. D. Palik, Ed.), p. 749. Academic Press, London. 1985. 23 Lines M. E., "Ultra low loss glasses," AT&T Bell Labs. Tech. Memo. TM 11535850916-33TM (1985). 24 Yeun M. J., "Ultraviolet absorption studies in germanium silicate glasses," Appl Opt. 21(1), 136-140 (1982). 25 Keck D. B., Maurer R. D., and Shultz P. C., "On the ultimate lower limit of attenuation in glass optical waveguides," Appl. Phys. Lett. 22, 307 (1973). 26 See, for example, SPIE 1516, and articles therein. 27 Georges T., Delevaque E., Monerie M., Lamouler P., and Bayon J. F., "Pair induced quenching in erbium doped silicate fibers," IEEE Optical Amplifiers and Their Applications, Technical Digest, 17, 71 (1992). 28 Ladoucer F. and Love J. D., in Silica-Based Channel Waveguides and Devices. Chapman & Hall, London (1996). 29 Williams D. L., Ainslie B. J., Armitage J. R., Kashyap R., and Campbell R. J., "Enhanced UV photosensitivity in boron codoped germanosilicate fibres," Electron Lett. 29, 1191 (1993). 30 Camlibel I., Pinnow D. A., and Dabby F. W., "Optical ageing characteristics of borosilicate clad fused silica core fiber optical waveguides." Appl. Phys. Lett. 26(4), 1183-1185 (1992). 31 Bansal N. P. and Doremus R. H., "Handbook of glass properties," Academic Press, New York, (1978). 32 Smith D. Y., "Dispersion theory, sum rules and their application to the analysis of optical data," in The Handbook of Optical Constants, (E. P. Palik, Ed.), Chapter 3. Academic Press, New York (1985). 33 Malitson I. H., "Interspecimen comparison of the refractive index of fused silica," J. Opt. Soc. Am. 15(10), 1205-1209 (1965). 34 Fleming J., "Dispersion in GeO2-SiO2 glasses," Appl. Opt. 23(4), 4486 (1984). 35 Hand D. P. and Russel P. St. J., "Photoinduced refractive index changes in germanosilicate optical fibers," Opt. Lett. 15(2), 102-104 (1990). 36 Data on fused quartz, Hareaus-Amersil Inc.

Ghapter

2

Photosensitivity and Photosensitization of Optical Fibers We have seen in the last chapter t h a t optical fibers have very good optical properties for light transmission. Electronic absorptions t h a t lead to attenuation are in the deep UV wavelength regime, and the molecular vibrations are far removed from the optical fiber transmission windows of interest to telecommunications. We have briefly considered the possible link between the change in absorption and the effect on the refractive index. Another possibility for the refractive index change is via an electrooptic nonlinearity. However, the symmetry properties of glass prohibit the electro-optic effect [1]. If there is an electro-optic contribution to the changes in the refractive index as a result of exposure to UV radiation, then an internal order would have to be created. This chapter considers aspects of defects connected with photosensitivity and techniques for photosensitization of optical fibers. We briefly compare in Section 2.1 the electro-optic effect [2] and how this may be invoked in glass. This aspect has recently received considerable interest worldwide but, as already stated, will not be studied in this book in any detail. Section 2.2 introduces some of the defects t h a t are linked to the UV-induced change in refractive index of glass. The hot debate on defects has continued for a n u m b e r of years and there are a vast n u m b e r of "subtleties" with regards to the same nominal defect state, as well as pathways to achieving transformations from one state to the other. Some of the defects cannot be detected 13

14

Chapter 2 Photosensitivity and Photosensitization of Optical Fibers

by optical means and require sophisticated methods. The task is not made easy by the various nomenclature used in labeling, so t h a t unraveling defects is made inaccessible to the layman. A simple overview of the important defects is given and we point to the literature for a detailed discussion [3,4]. Section 2.3 looks at the evidence of photoexcitation of electrons and, in conjunction with Section 2.2, the methods for the detection of defects. The routes used to photosensitize and fabricate fibers are presented in the last section.

2.1

Photorefractivity and photosensitivity

It is useful to distinguish the term photorefractivity from photosensitivity and photochromic effect. Photorefractivity refers to a phenomenon usually ascribed to crystalline materials that exhibit a second-order nonlinearity by which light radiation can change the refractive index by creating an internal electric field [5]. Photosensitivity invariably refers to a permanent change in refractive index or opacity induced by exposure to light radiation with the internal field playing an insignificant role. The term traditionally applies to the color change in certain glasses with exposure to ultraviolet radiation and heat. Photochromic glass does not depend on the application of heat to change opacity, and the action is reversible. However, a combination of these properties is possible in glasses and is a novel phenomenon, which is currently being studied, not least because it is poorly understood. Considering the normal polarization response of materials to applied electric fields may provide a physical insight into the phenomenon of photorefractivity and poling of glass. The induced polarization, P, in a medium can be described by the relationship D = soE + P,

(2.1.1)

where D is the displacement, E is the applied field, ~o is the free space permittivity, and P is the induced polarization. In a material in which the polarization is nonlinear, the polarization may be expanded in powers of the applied field as P = ~oA)l)E + t~oA)2)E2 -+- t~oA)3)E3 + . . . = So{A)l)E + 22)E 2 + 23)E 3 + . . . }

(2.1.2)

2.1.

Photorefractivity and photosensitivity

15

and D t~r

t~oE

-

1 + X (1),

(2.1.3)

where Sr = 1 + X(1) is the linear permittivity, X(2) is the first t e r m of the nonlinear susceptibility (which can be nonzero in crystalline media), and X(3) is the third-order nonlinearity (nonzero in all materials). Using Equations (2.1.2) and (2.1.3), the perturbed permittivity u n d e r the influence of an applied electric field is D -

-

t~r ~- ) ~ 2 ) E

+ 2~3)E2 . . .

= s~ + As = s,

(2.1.4) (2.1.5)

and since the refractive index n is related to the permittivity as s=n

2

= (n o + An) 2, ~n~ + 2nohn

(2.1.6)

from which immediately follows An = ~ 1 [22)E + 23>E 2 . . . ] .

(2.1.7)

In photorefractive materials with an active ~2), an internal charge can build up due to trapped carriers released from defects. These give rise to an internal field, which modulates the refractive index locally via the first t e r m in Eq. (2.1.7). The induced index changes result directly from the linear electro-optic effect (X(2)) and are in general quite large, ~"10 -4. However, with X (2) being zero in glass, the induced refractive index with an applied field can only result from the nonzero third-order susceptibility, X(3). Even if an internal field could develop, the refractive index change is small, ~10-7; however, as will be seen, if an internal field is possible in glass, it results in a modest nonlinearity [2]. We now a s s u m e the existence of an internal field Edc and apply an external field Eapplie d. The induced index change is as follows: An = ~

1

~3)(Edc +

Eapplied) 2

2 = n~(E~c + 2Edc X Eapplie d + Eapplied).

(2.1.8) (2.1.9)

16

Chapter 2 Photosensitivity and Photosensitization of Optical Fibers

The first term in Eq. (2.1.9) indicates a p e r m a n e n t index change, whereas the third term is the usual quadratic nonlinear effect known as the dcKerr effect. We have used a prime on the n~, to distinguish it from the optical Kerr constant n2. The interesting relationship is described by the remaining term, An = 2n~Edc X Eapplie d.

(2.1.10)

This relationship is analogous to the linear electro-optic effect, in which the applied field operates on an enhanced nonlinearity, 2n~ Edc , due to the frozen internal field. If the internal field is large, then a useful nonlinearity is possible. This effect is believed to be partly the basis of poled glass [2]. In crystalline media with a large photorefractive response, the nonlinearity ;{2) is several orders of magnitude larger than the next higher order coefficient, ;{3) (and hence n~) in glass. From the first term in Eq. (2.1.9) we can calculate the required field for a change in the refractive index of 10 -3. With a measured value o f ~ 3) - 10 -22 m-2V -2 for silica, a large internal field o f - 1 0 9 V/m would be necessary, equivalent to n~ o f - 1 pm V -i. These values have been exceeded in UV photoelectrically poled fiber, with the highest reported result of ~ 6 pm/V [6]! Combined with the low dielectric constant of silica, it has a potentially large bandwidth for electrooptic modulation. Just how such a large field may develop has been debated. However, it has been suggested by Myers et al. [7,8] t h a t the poling voltage is dropped across a thin layer ( - 5 / ~ m ) within the glass, causing huge fields to appear. The electro-optic nature ofUV photoinduced refractive index in Bragg gratings has not been reported, although the presence charges related to defects could indeed develop an internal field, as in the case of secondharmonic generation in glass [9]. In the next section, we consider some of the important defects, which are of interest in unraveling the mystery of photosensitivity of glass.

2.2

Defects

in glass

The nature of fabrication of glass is ideally suited to promoting defects. The chemical reactions that take place in a modified chemical vapor deposition (MCVD) [10] process are based on hot gases reacting to form a soot deposit on the inside of a silica support tube or on the outside in outside vapor phase deposition (OVD). The process allows the ratio of reactive gases such as silicon/germanium tetrachloride and oxygen to be

2.2.

Defects in glass

17

easily changed to arrive at a nearly complete chemical reaction, depositing a mixture of germanium and silicon dioxides. It is not possible to have a 100% reaction, so the deposited chemicals have a proportion of suboxides and defects within the glass matrix. With sintering and preform collapse, these reaction components remain, although further alterations may take place while the fiber is being drawn, when bonds can break [11-13]. The end result is a material that is highly inhomogeneous on a microscopic scale with little or no order beyond the range of a few molecular distances. The fabrication process also allows other higher-order ring structures [ 14] to form, complicating the picture yet further. There is a possibility of incorporating not only a strained structure, but also one which has randomly distributed broken bonds and trapped defects. This is especially true of a fiber with the core dopant germanium, which readily forms suboxides as GeOx (x = 1 to 4), creating a range of defects in the tetrahedral matrix of the silica host glass. Given this rich environment of imperfection, it is surprising t h a t state-of-the-art germania-doped silica fiber has extremely good properties--low loss and high optical damage t h r e s h o l d - - a n d is a result of better understanding of defects, which lead to increased attenuation in the transmission windows of interest. Among the well-known defects formed in the germania-doped silica core are the paramagnetic Ge(n) defects, where n refers to the number of next-nearest-neighbor Ge/Si atoms surrounding a germanium ion with an associated unsatisfied single electron, first pointed out by Friebele et al. [17]. These defects are shown schematically in Fig. 2.1. The Ge(1) and Ge(2) have been identified as trapped-electron centers [18]. The GEE', previously known as the Ge(0) and the Ge(3) centers, which is common in oxygen-deficient germania, is a hole trapped next to a germanium at an oxygen vacancy [19] and has been shown to be independent of the number of next-neighbor Ge sites. Here an oxygen atom is missing from the tetrahedron, while the germania atom has an extra electron as a dangling bond. The extra electron distorts the molecule of germania as shown in Fig. 2.2. The GeO defect, shown in Fig. 2.2 (LHS), has a germanium atom coordinated with another Si or Ge atom. This bond has the characteristic 240-nm absorption peak that is observed in many germanium-doped photosensitive optical fibers [21]. On UV illumination, the bond readily breaks, creating the GeE' center. It is thought t h a t the electron from the GeE' center is liberated and is free to move within the glass matrix via hopping or tunneling, or by two-photon excitation into the conduction

18

Chapter 2 Photosensitivity and Photosensitization of Optical Fibers

F i g u r e 2 . 1 : A schematic of proposed Ge (or Si) defects of germania-doped silica. The characteristic absorption of the Ge(1) is -280 nm (4.4 eV) [18] and is a trapped electron at a Ge (or Si) site; Ge(2) has an absorption at 213 nm (5.8 eV) and is a hole center. The peroxy radical has an absorption at 7.6 eV (163 nm) and at 325 nm (3.8 eV) [15,16].

band [22-24]. This electron can be r e t r a p p e d at the original site or at some other defect site. The removal of this electron, it is believed, causes a reconfiguration of the shape of the molecule (see Fig. 2.2), possibly also changing the density of the material, as well as the absorption. It appears t h a t the Ge (1) center is the equivalent of the g e r m a n i u m defects observed in a-quartz, k n o w n as the Ge(I) and Ge(II), b u t less well defined [23]. P h o s p h o r u s forms a series of defects similar to those of germanium. However, the photosensitivity is limited at 240 n m and requires shorter wavelengths, such as 193-nm radiation [24]. Other defects include the nonbridging oxygen hole center (NBOHC), which is claimed to have absorptions at 260 and 600 nm, a n d the peroxy

2.3.

19

Detection of defects

F i g u r e 2 . 2 : The GeO defect of germania-doped silica, in which the atom adjacent to germanium is either a silicon or another germanium. It can absorb a photon to form a GeE' defect. The Ge(0) or Ge(3) are a GeE' center [20]. The GeE' defect shows the extra electron (associated with the Ge atom), which may be free to move within the glass matrix until it is retrapped at the original defect site, at another GeE' hole site, or at any one of the Ge(n) defect centers.

radical (P-OHC) [25], believed to absorb at 260 nm. Both are shown in Fig. 2.1.

2.3

Detection

of defects

A considerable a m o u n t of work h a s b e e n done in u n d e r s t a n d i n g defects in glass. Detection of defects m a y be broadly categorized into four groups: optically active defects can be observed because of t h e i r excitation spect r u m or excitation a n d luminescence/fluorescence s p e c t r u m while optically inactive defects are detectable by t h e i r electron spin r e s o n a n c e signature, or E S R spectrum, t o g e t h e r w i t h optical emission spectrum. The model of t h e defects as shown in Fig. 2.2 suggests t h e liberation of electrons on absorption of UV radiation. It should therefore be possible to detect l i b e r a t e d charges e x p e r i m e n t a l l y ; since silica h a s a h i g h volume resistivity, it is n e c e s s a r y to choose a g e o m e t r y t h a t can directly enable t h e m e a s u r e m e n t of electric currents. P h o t o s e n s i t i v i t y h a s been explored

20

Chapter 2 Photosensitivity and Photosensitization of Optical Fibers

both indirectly, e.g., by etching glass exposed to radiation or using secondharmonic generation [9,26,27] as a probe, and directly, e.g., by measurement of photocurrent in germania-doped planar waveguides [28] and across thin films of bulk glass [29]. It has been concluded that the photocurrent is influenced by the fluence of the exciting UV radiation; the photocurrent (probably by tunneling [29]) is a linear function of the power density for CW excitation [28], while for pulsed, high-intensity radiation, it takes on a two-photon excitation characteristic [29]. The paramagnetic defects of the Ge(n) type including the E' center are detected by ESR. The GeE' has an associated optical absorption at 4.6 eV [30].

2.4

Photosensitization

techniques

A question often asked is: Which is the best fiber to use for the fabrication of most gratings? Undoubtedly, the preferred answer to this question should be standard telecommunications fiber. Although techniques have been found to write strong gratings in this type of fiber, there are several reasons why standard fiber is not the best choice for a number of applications. Ideally, a compatibility with standard fiber is desirable, but the design of different devices requires a variety of fibers. This does open the possibility of exploiting various techniques for fabrication and sensitization. Here we look in some detail at the behavior of commonly used species in optical fiber and present their properties, which may influence the type of application. For example, the time or intensity of UV exposure required for the writing of gratings affects the transmission and reliability properties. This results in either damage (Type II gratings) [31] or the formation of Type I, at low fluence, and Type IIA gratings [32], each of which have different characteristics (see Section 2.4.1). The use of boron and tin as a codopant in germanosilicate fibers, hot hydrogenation and cold, high-pressure hydrogenation, and flame-assisted low-pressure hydrogenation ("flame-brushing") are well-established photosensitization methods. The type of the fiber often dictates what type of grating may be fabricated, since the outcome depends on the dopants. The literature available on the subjects of photosensitivity, the complex nature of defects, and the dynamics of growth of gratings is vast

2.4.

21

Photosensitization techniques

[34]. The sheer n u m b e r s of different fibers available worldwide, f u r t h e r complicates the picture and by the very n a t u r e of the limited fiber set available within the framework of a given study and the complex n a t u r e of glass, comparisons have been extremely difficult to interpret. This is not a criticism of the research in this field, merely a s t a t e m e n t r e i t e r a t i n g the dilemma facing researchers: how to deal with far too m a n y variables! In order to draw conclusions from the available data, one can simply suggest a trend for the user to follow. A choice m a y be made from the set of commonly available fibers. For a certain set of these fibers (e.g., s t a n d a r d telecommunications fiber) the method for photosensitization m a y be simply hydrogenation, or 193-nm exposure. It is often the availability of the laser source t h a t dictates the approach.

2.4.1

Germanium-doped

silica fibers

Photosensitivity of optical fibers has been correlated with the concentration of GeO defects in the core [33,34]. The presence of the defect is indicated by the absorption at 240 nm, first observed by Cohen and Smith [35] and attributed to the reduced g e r m a n i a state, Ge(II). The n u m b e r of these defects generally increases as a function of Ge concentration. Figure 2.3 shows the absorption at 242 n m in a perform with the germa-

F i g u r e 2.3: Absorption at 242 nm in preform samples before and after collapse as a function of Ge concentration (after Ref. [36]).

22

Chapter 2

Photosensitivity and Photosensitization of Optical Fibers

nium concentration [36]. The slope in this graph is - 2 8 dB/(mm-mol%) of Ge before the preform sample is collapsed (dashed line). After collapse, the number of defects increases, and the corresponding absorption changes to ~36 dB/(mm-mol%) (Fig. 2.3 continuous line). Increasing the concentration of defects increases the photosensitivity of the fiber. This can be done by collapsing the fiber in a reducing atmosphere, for example, by replacing oxygen with nitrogen or helium [36] or with hydrogen [37,49]. The 240-nm absorption peak is due to the oxygen-deficient hole center defect, (Ge-ODHC) [38] and indicates the intrinsic photosensitivity. It can be quantified as [39] k = a242 nm/C,

(2.4.1)

where ~242 nm is the absorption at 242 nm and C is the molar concentration of GeO2. Normally C lies between 10 and 40 dB/(mm-mol% GeO2). Hot hydrogenation is performed on fibers or preforms at a temperature of -650~ for 200 hours is 1 atm hydrogen [40]. The absorption at 240 nm closely follows the profile of the Ge concentration in the fiber [33], and k has been estimated to be large, - 1 2 0 dB/(mm-mol% GeO2). The saturated UV-induced index change increases approximately linearly with Ge concentration after exposure to UV radiation, from - 3 x 10 -5 (3 mol% GeO%2) for standard fiber to - 2 . 5 • 10 -4 ( - 2 0 mol% GeO2) concentration, using a CW laser source operating at 244 nm [49]. However, the picture is more complex t h a n the observations based simply on the use of CW lasers. With pulsed laser sources, high-germania-doped fiber (8%) shows an the initial growth rate of the UV-induced refractive index change, which is proportional to the energy density of the pulse. For low germania content, as in standard telecommunications fiber, it is proportional to the square of the energy density. Thus, two-photon absorption from 193 nm plays a crucial role in inducing maximum refractive index changes as high as - 0 . 0 0 1 in standard optical fibers [41]. Another, more complex phenomenon occurs in untreated germania fibers with long exposure time, in conjunction with both CW and pulsed radiation, readily observable in high germania content fibers [47]. In high-germania fiber, long exposure erases the initial first-order grating completely, while a second-order grating forms. This erasure of the first-order and the onset of second-order gratings forms a demarcation between Type I and Type IIA gratings.

2.4.

Photosensitization techniques

23

Increasing the energy density damages the fiber core, forming Type II gratings [31]. The thermal history of the fiber is also of great importance, as is the mechanical strain during the time of grating inscription. Significantly, even strains as low as 0.2% can increase the peak refractive index modulation of the Type IIA grating in high g e r m a n i u m content fiber [42,43]. High-germania-doped (30%Ge) fibers drawn under high pulling tension show the opposite behavior [44], indicating the influence of elastic stress during drawing rather t h a n the effect of drawing-induced defects [45]. Annealing the fiber at ll00~ for 1 hour and then cooling over 2 days reduces the time for the erasure of the Type I grating, as well as increasing the m a x i m u m refractive index modulation achievable in the Type IIA regime. With tin as a codopant in high-germanium fiber, the general overall picture changes slightly, but the dynamics are similar, except for reduced index change under strained inscription [46]. Thus, absolute comparison is difficult, and one may use the germania content as an indicator, bearing in mind the complex n a t u r e of the dynamics of grating formation in germania-doped silica fiber. Typical results for a high-germania fiber are shown in Fig. 2.4. The growth of the refractive index modulation as a function of time stops in the case of all three fibers shown, dropping to zero before increasing once again to form Type IIA gratings. Photosensitivity of fiber fabricated under reduced conditions as a function Ge concentration also increases, but it is not sufficient to interpret the data by the m a x i m u m index change. The reason for this is the induction of Type IIA gratings [47] in relatively low concentration of Ge. Measurements performed under pulsed conditions reveal t h a t the onset of the Type IIA grating is almost certainly always possible in any concentration of Ge; only the time of observation increases with low concentrations, although for practical purposes this time may be too long to be of concern. Figure 2.5 shows data from the growth of the average index on UV exposure as a function of Ge concentration in fibers, which have been reduced. The m a x i m u m index should change monotonically; however, above a certain concentration, the onset of Type IIA forces the observed m a x i m u m index change for point B (20 mol% Ge), since the grating being written slowly disappears before growing again. While the m a x i m u m reflectivity should increase to higher levels, within the time frame of the measurements this fiber appears to be less sensitive. A better indicator is the initial growth rate of the index change, since Type IIA grating is not observed for some time into the measurements. Figure 2.5 shows an

24

Chapter 2 Photosensitivity and Photosensitization of Optical Fibers 0.002

Ge-Sn doped fiber L=2.5mm; ~B=1535rma; I=26W/cm 2 B Af~

Anneal

C

/

t.O i

//

Slrained Fiber

/)

I

"0

ZkL/L=2.10-3/

)/

0

E

,

O (D

/

/

\

'd\ /)

f:}.

E
3fold in the UV-induced refractive index modulation as well as an order of magnitude reduction in the writing time. With respect to 10 mol% reduced germanium fiber, the improvement in the maximum refractive index modulation is - 4 0 % with a • 6 reduction in the writing time. The maximum refractive index change is close to 10 -3 for this fiber induced with a CW laser operating at 244 nm [54]. A point worth noting with B-Ge fibers is the increased stress, and consequently, increased induced birefringence [59]. The preforms are difficult to handle because of the high stress. However, the real advantages with B-Ge fibers are the shortened writing time, the larger UV-induced refractive index change, and, potentially, fibers that are compatible with any required profile, for small-core large NA fiber amplifiers, to standard fibers. B-Ge fibers form Type IIA gratings [60] with a CW 244-nm laser, as is the case with the data shown in Fig. 2.4. This suggests that there is probably little difference due to the presence of boron; only the high germanium content is responsible for this type of grating. There is a possibility that stress is a contributing factor to the formation of Type IIA [61]; recent work does partially indicate this but for germanium-doped fibers [44]. Typically, gratings written with CW lasers in B-Ge fiber decay more rapidly than low germanium doped (5 mol%) fibers when exposed to heat. Gratings lose half their index modulation when annealed at -400~ (BGe: 22:6.3 mol%) and -650~ (Ge 5 mol%) [46] for 30 minutes. A detailed

2.4.

Photosensitization techniques

29

study of the decay of gratings written in B-Ge may be found in Ref. [62]. The thermal annealing of gratings is discussed in Chapter 9. Boron causes additional loss in the 1550-nm window, of the order of ~-0.1 dB/m, which may not be desirable. For short gratings, this need not be of concern.

2.4.3

Tin-germanium codoped fibers

Fabrication of Sn codoped Ge is by the MCVD process used for silica fiber by incorporating SnC14 vapor. SnO2 increases the refractive index of optical fibers and, used in conjunction with GeO2, cannot be used as B203 to match the cladding refractive index, or to enhance the quantity of germanium in the core affecting the waveguide properties. However, it has three advantages over B-Ge fiber: The gratings survive a higher temperature, do not cause additional loss in the 1500-nm window, have a slightly increased UV-induced refractive index change, reported to be 3 times larger t h a n that of B-Ge fibers. Compared with B-Ge, Sn-Ge fibers lose half the UV-induced refractive index change at -600~ similarly to standard fibers [63].

2.4.4

Cold, h i g h - p r e s s u r e h y d r o g e n a t i o n

The presence of molecular hydrogen has been shown to increase the absorption loss in optical fibers over a period of time [64]. The field was studied extensively [65], and it is known t h a t the hydrogen reacts with oxygen to form hydroxyl ions. The increase in the absorption at the first overtone of the OH vibration at a wavelength of 1.27 /~m was clearly manifest by the broadband increase in loss in both the 1300-nm and, to a lesser extent, in the 1500-nm windows. Another effect of hydrogen is the reaction with the Ge ion to form GeH, considerably changing the band structure in the UV region. These changes, in turn, influence the local refractive index as per the Kramers-Kronig model. The reaction rates have been shown to be strongly temperature dependent [65]. It has been suggested t h a t the chemical reactions are different on heat t r e a t m e n t and cause the formation of a different species compared to illumination with UV radiation. However, no noticeable increase in the 240-nm band is observed with the presence of interstitial molecular hydrogen in Gedoped silica. The highest refractive index change induced by UV radiation is undoubtedly in cold hydrogen soaked germania fibers. As has been

30

Chapter 2 Photosensitivity and Photosensitization of Optical Fibers

seen, an atmosphere of hot hydrogen during the collapse process or hot hydrogen soaking of fibers enhances the GeO defect concentration [37]. The presence of molecular hydrogen has been known to induce increases in the absorption loss of optical fibers, since the early day of optical fibers [50]. Apart from being a nuisance in submarine systems, in which hydrogen seeps into the fiber, causing a loss that increases with time of exposure, cold high pressure hydrogen soaking has led to germaniumdoped fibers with the highest observed photosensitivity [66]. Any germania-doped fiber may be made photosensitive by soaking it under high pressure (800 bar) and/or high temperature (< 150~ Molecular hydrogen in-diffuses to an equilibrium state. The process requires a suitable highpressure chamber into which fibers may be left for hydrogen loading. Once the fiber is loaded, exposure to UV radiation is thought to lead to a dissociation of the molecule, leading to the formation of Si-OH and/or Ge-OH bonds. Along with this, there is formation of the Ge oxygendeficient centers, leading to a refractive index change. Soaking the fiber at 200 bar at room temperature for - 2 weeks is sufficient to load the 125-micron diameter fiber at 21~ [66]. UV exposure of standard hydrogen fibers easily yields refractive index changes in excess of 0.011 [67] in standard telecommunications fiber, with a highest value of 0.03 inferred [68]. Almost all Ge atoms are involved in the reactions giving rise to the index changes. Figure 2.8 shows the changes in the refractive index profile of a standard fiber before and after exposure to pulsed UV radiation at 248 nm ( - 6 0 0 mJ/cm 2, 20 Hz, 60minute exposure) [68]. The growth of gratings is long with CW lasers (duration of 20 minutes for strong gratings with refractive index changes o f - 1-2 x 10-3). The picture is quite different with the growth kinetics when compared with non-hydrogen-loaded germania fibers. To date, Type IIA gratings have not been observed in hydrogen-loaded fibers. There is also no clear evidence of the stress dependence of grating growth [44]. Whereas in Type IIA the average UV-induced refractive index change is negative, in hydrogen-loaded fibers the average refractive index grows unbounded to large values (>0.01). Heating a hydrogen-loaded fiber increases the refractive index rapidly, even in P205 and P205:A1203-doped multimode fibers [68], although pure silica is not sensitized. The dynamic changes that occur in the process of fiber grating fabrication are complex. Even with hydrogen-loaded fibers, there are indications that as the grating grows, the absorption in the core increases in the UV,

2.4.

31

Photosensitization techniques 0.02

|

i

......... U n t r e a t e d UV exposed

X c> .m

O.01

~

0 r

:...

(1)

rr

0.00 i

i

-30 -20 -10

i

o

i

10

i

20

30

Fiber radius (lzn)

F i g u r e 2 . 8 : The refractive index profile of a 2.8% hydrogen-soaked standard fiber, before and after UV exposure with pulsed radiation at 248 nm (Courtesy P. Lemaire from: Lemaire P. J., Vengsarkar A. M., Reed W. A., and Mizarhi V., "Refractive index changes in optical fibers sensitized with molecular hydrogen," in Technical Digest of Conf. on Opt. Fiber Commun., 0FC'94, pp. 47-48, 1994.)

as does the 4 0 0 - n m l u m i n e s c e n c e [69]. Martin et al. [69] h a v e found a direct correlation b e t w e e n refractive index change increase and luminescence. Figure 2.9 shows the t r a n s m i s s i o n spectra of two gratings in hydrogenated standard fiber at different stages of growth, with the U V radiation at 244 n m CW switched on and off. With the U V switched on, the Bragg

O

~1

.~ -10 ~. - 1 5

i

.

-20 Wavelength,

nm

F i g u r e 2 . 9 : Shift in the Bragg wavelength as the UV radiation is switched on and off for two different strength gratings (after Ref. [70]).

32

Chapter 2 Photosensitivity and Photosensitization of Optical Fibers

wavelength shifts 0.05 nm to longer wavelengths at a grating reflectivity o f - 1 . 4 dB. When the grating has grown to - 2 7 dB (different grating but same fiber), the shift is 0.1 nm, equivalent to an equilibrium temperature increase of the fiber of-80~ At the start of grating growth (97% fabricated through polymer jacket using near-UV radiation," in Bragg Gratings, Photosensitivity, and Poling in Glass Fibers and Waveguides: Applications and Fundamentals, Vol. 17, OSA Technical Digest Series (Optical Society of America, Washington, DC, 1997), post-deadline paper PD1. 72 Vengsarkar A. M., Lemaire P. J., Judkins J. B., Bhatia V., Erdogan T., and Sipe J. E., "Long period fiber gratings as band rejection filters," IEEE J. Lightwave. Technol. 14, 58-64 (1996). 73 Stubbe R., Sahlgren B., Sandgren S., and Asseh A., "Novel technique for writing long superstructured fiber Bragg gratings," in Photosensitivity and Quadratic Nonlinearity in Glass Waveguides: Fundamentals and Applications, Vol. 22, 1995 OSA Technical Series (Optical Society of America, Washington, DC, 1995), pp. PDI-(1-3) (1995). 74 Kashyap R., Froehlich H-G., Swanton A., and Armes D.J., "Super-stepchirped fibre Bragg gratings," Electron. Lett. 32(15), 1394-1396 (1996). 75 Kashyap R., Froehlich H-G., Swanton A., and Armes D. J., "1.3 m long superstep-chirped fibre Bragg grating with a continuous delay of 13.5 ns and bandwidth 10 nm for broadband dispersion compensation," Electron. Lett. 32(19), 1807-1809 (1996). 76 Zhang Q., Brown D. A., Reinhart L., Morse T. F., Wang J. Q., and Xiao G., "Tuning Bragg wavelength by writing gratings on prestrained fibers," IEEE Photon. Technol. Lett. 6(7), 839-841 (1994).

114

Chapter 3 Fabrication of Bragg Gratings

77 Legoubin S., Fertein E., Douay M., Bernage P., Niay P., Bayon F., and Georges T., "Formation of Moir~ gratings in core ofgermanosilicate fibre by transverse holographic double exposure," Electron. Lett. 27(21), 1945 (1991). 78 Sugden K., Zhang L., Williams J. A. R., Fallon L. A., Everall L. A., Chisholm K. E., and Bennion I., "Fabrication and characterization of bandpass filters based on concatenated chirped fiber gratings," IEEE J. Lightwave Technol. 15(8), 1424-1432 (1997). 79 Byron K. C., Sugden K., Bircheno T., and Bennion I., "Fabrication of chirped Bragg gratings in photosensitive fibre," Electron. Lett. 29(18), 1659 (1993). 80 Putnam M. A., Williams G. M., and Friebele E. J., "Fabrication of tapered, strain-gradient chirped fibre Bragg gratings," Electron. Lett. 31(4), 309-310 (1995). 81 Martin J., Lauzon J., Thibault S., and Ouellette F., "Novel writing technique of long highly reflective in fiber gratings and investigation of the linearly chirped component," post-deadline paper PD29-1, 138, Proc. Conference on Optical Fiber Communications, 0FC'94 (1994). 82 Morey W. W., Meltz G., and Glenn W. H.,"Fiber optic Bragg grating sensors," SPIE 1169, Fibre Optics Sensors VII, pp. 98-107 (1989). 83 Kringlebotn J. T., Morkel P. R., Reekie L., Archambault J. L., and Payne D.N., "Efficient diode-pumped single frequency erbium:ytterbium fibre laser," IEEE Photon. Technol. Lett. 5(10), 1162 (1993). 84 Canning J. and Skeats M. G., "Tr-Phase shifted periodic distributed structures in optical fibers by UV post-processing," Electron. Lett. 30(16), 1244-1245 (1994). 85 Agrawal G. P. and Radic S., "Phase-shifted fiber Bragg gratings and their applications for wavelength demultiplexing," IEEE Photon. Technol. Lett. 6, 995-997 (1994). 86 Jayaraman V., Cohen D. A., and Coldren L. A., "Demonstration of broadband tunability of a semiconductor laser using sampled gratings," Appl. Phys. Lett. 60(19), 2321-2323 (1992). 87 Eggleton B. J., Krug P. A., Poladin L., and Ouellette F., "Long periodic superstructure Bragg gratings in optical fibres," Electron. Lett. 30(19), 1620-1621 (1994). 88 Ouellette F., Krug P.A., and Pasman R., "Characterisation of long phase masks for writing fibre Bragg gratings," in Photosensitivity and Quadratic Nonlinearity in Glass Waveguides: Fundamentals and Applications, Vol. 22, 1995 OSA Technical Series (Optical Society of America, Washington, DC, 1995), pp. 116-119.

References

115

89 Legoubin S., Douay M., Bernage P., Niay, Boj S., and Delevaque E., "Free spectral range variations of grating-based Fabry-Perot photowritten in optical fibers," J. Opt. Soc. Am. A 12(8), 1687-1694 (1995). 90 Zengerle R. and Leminger O., "Phase-shifted Bragg-grating filters with improved transmission characteristics," J. Lightwave Technol. 13, 2354-2358 (1995). 91 StorOy H., Engan H. E., Sahlgren B., and Stubbe R., "Position weighting of fibre Bragg gratings for bandpass filtering," Opt. Lett. 22(11), 784-786 (1997). 92 Kashyap R, McKee P. F., and Armes D., "UV written reflection grating structures in photosensitive optical fibres using phase-shifted phase-masks," Electron. Lett. 30(23), 1977-1979 (1994). 93 Ibsen M., Eggleton B. J., Sceats M. G., and Ouellette F., "Broadly tunable DBR fibre using sampled Bragg gratings," Electron. Lett. 31(1), 37-38, (1995). 94 Byron K. C., Sugden K., Bircheno T., and Bennion I., "Fabrication of chirped Bragg gratings in a photo sensitive fibre," Electron. Lett. 29(18), 1659-1660 (1993). 95 Krug P. A., Stephens T., Yoffe G., Ouellette F., Hill P., and Doshi G., "270 km transmission at 10Gb/s in nondispersion shifted fiber using an adjustably chirped 120 mm long fiber Bragg grating dispersion compensator," in Tech. Digest Conf. on Opt. Fiber Commun., 0FC'95, post-deadline paper PDP27 (1995). 96 Kashyap R., McKee P. F., Campbell R. J., and Williams D. L., "A novel method of writing photo-induced chirped Bragg gratings in optical fibres," Electron. Lett. 12, 996-998 (1994). 97 Delavaque E., Boj S., Bayon J-F., Poignant H., Le Mellot J., Monerie M., Niay P., and Bernage P., "Optical fiber design for strong grating photo imprinting with radiation mode suppression," in Proc. Post-Deadline Papers of 0FC'95, paper PD5 (1995). 98 Sugden K., Bennion I., Moloney A., and Cooper N. J., "Chirped grating produced in photosensitive optical fibres by fibre deformation during exposure," Electron. Lett. 30(5), 440-441 (1994). 99 Dong L., Cruz J. L., Reekie L., and Trucknott J. A., "Fabrication of chirped fibre gratings using etched tapers," Electron. Lett. 31(11), 908-909 (1995). 100 Dong L., Cruz J. L., Reekie L., and Trucknott J. A., "Chirped fiber Bragg gratings fabricated using etched tapers," Opt. Fiber Technol. 1, 363-368 (1995). 101 Okude S., Sakai T., Wada A., and Yamauchi R., "Novel chirped fiber grating utilizing a thermally diffused taper-core fiber," in Proc. 0FC'96, paper TuO7, pp. 68-69 (1996).

116

Chapter 3 Fabrication of Bragg Gratings

102 Shiraishi K., Aizawa Y., and Kawakami S., J. Lightwave Technol. 8, 1151 (1990). 103 Byron K. C. and Rourke H. N., "Fabrication of chirped fibre gratings by novel stretch and write technique," Electron. Lett. 31(1), 60-61 (1995). 104 Farries M. C., Sugden K, Reid D. C. J., Bennion I., Molony A., and Goodwin M. J., "Very broad reflection bandwidth (44 nm) chirped fibre gratings and narrow-bandpass filters produced by the use of an amplitude mask," Electron. Lett. 30(11), 891-892 (1994). 105 Kashyap R., "Design of step-chirped fibre Bragg gratings," Opt. Comm., 136(5-6), 461-469 (1997). 106 Kashyap R., Chernikov S. V., Mckee P. F., and Taylor J. R., "30 ps chromatic dispersion compensation of 400 fs pulses at 100 Gbits/s in optical fibres using an all fibre photoinduced chirped reflection grating," Electron. Lett. 30(13), 1078-1079 (1994). 107 Kawase L. R., Carvalho M. C. R., Margulis W., and Kashyap R., "Transmission of chirped optical pulses in fibre-grating dispersion compensated system," Electron. Lett. 33(2), pp. 52-54 (1997). 108 Kashyap R., Swanton A., and Armes D. J., "A simple technique for apodising chirped and unchirped fibre Bragg gratings," Electron. Lett. 32(14), 1227-1228 (1996). 109 Riant I. and Sansonetti P., "New method to control chirp and wavelength of fibre Bragg gratings for multichannel chromatic dispersion compensation", in Colloquium on Optical Fibre Gratings, IEE Ref., 1997/037, pp. 18/1-18/3, London (1997). 110 Kashyap R., Maxwell G. D., and Ainslie B. J., "Laser-trimmed four-port bandpass filter fabricated in single-mode photosensitive Ge-doped planar waveguide," IEEE J. Photon. Technol. 5(2), 191-194 (1993). 111 Kashyap R., unpublished. 112 Kashyap R., Ellis A., Malyon D., Froehlich H-G., Swanton A., and Armes D. J., "Eight wavelength x 10Gb/s simultaneous dispersion compensation over 100km singlemode fibre using a single 10 nm bandwidth, 1.3 metre long, super-step-chirped fibre Bragg grating a continuous delay of 13.5 ns," in Proc. Post-Deadline Papers of the 22nd ECOC'97, Oslo, Norway, Sept. 15-19, 1996. 113 Archambault J-L., Ph.D. Thesis, Southampton University, United Kingdom (1994). 114 Xie W. X., Niay P., Bernage P., Douay M., Bayon J. F., Georges T., Monerie M., and Poumellec B., "Experimental evidence of two types of photorefractive

References

117

effects occurring during photoinscription of Bragg gratings within germanosilicate fibers," Opt. Commun. 104, 185-195 (1993). 115 Duval Y., Kashyap R., Fleming S., and Ouellette F., "Correlation between ultraviolet-induced refractive index change and photoluminescence in Gedoped fibre," Appl. Phys. Lett. 61(25) 2955 (1992). 116 Limberger H. G., Limberger P. Y., and Salath~ R., "Spectral characterization of photoinduced high efficient Bragg gratings in standard telecommunication fibers," Electron. Lett., 29(1), 47-49 (1993). 117 Kashyap R. and Maxwell G. D., unpublished (1991). 118 Askins C. G., Tsai T-E., Williams G. M., Puttnam M. A., Bashkansky M., and Friebele E. J., "Fibre Bragg reflectors prepared by a single excimer pulse," Opt. Lett. 17(11), 833 (1992). 119 Archambault J-L., Reekie L., and Russell P. St. J., "High reflectivity and narrow bandwidth fibre gratings written by a single excimer pulse," Electron. Lett. 29(1), 28 (1993). 120 Malo B., Johnson D. C., Bilodeau F., Albert J., and Hill K. O., "Single-excimerpulse writing of fiber gratings by use of a zero-order nulled phase mask: grating spectral response and visualization of index perturbations," Opt. Lett. 18(15), 1277 (1993). 121 Archambault J-L., Reekie L., and Russell P. St. J., "100% reflectivity Bragg reflectors produced in optical fibres by single excimer pulses," Electron. Lett. 29(5), 453 (1993). 122 Askins C. G., Putnam M. A., Williams G. M., and Friebele E. J., "Steppedwavelength optical-fiber Bragg grating arrays fabricated in line on a draw tower," Opt. Lett. 19(2), 147-149 (1994). 123 Dong L., Archambault J. L., Reekie L., Russell P. St. J., and Payne D. N., "Single pulse Bragg gratings written during fibre drawing," Electron. Lett. 29(17), 1577 (1993). 124 Mizrahi V. and Sipe J. E., "Optical properties of photosensitive fiber phase gratings," Lightwave Technol. 11(10), 1513-1517 (1993). 125 Dong L., Archambault J. L., Reekie L., Russell P. St. J., and Payne D. N., "Single pulse Bragg gratings written during fibre drawing," Electron. Lett. 29(17), 1577 (1993). 126 Patrick H., and Gilbert S. L., "Growth of Bragg gratings produced by continuous-wave ultra-violet light in optical fiber," Opt. Lett. 18(18), 1484 (1993). 127 Armitage J. R., "Fibre Bragg reflectors written at 262 nm using frequency quadrupled Nd3+:YLF, " Electron. Lett. 29(13), 1181-1183 (1993). 128 Dianov E. M., and Starodubov D. S., "Microscopic mechanisms of photosensitivity in germanium-doped silica glass," SPIE Proc, 2777, pp. 60-70 (1995).

118

Chapter 3 Fabrication of Bragg Gratings

129 Starodubov D. S., Dianov E. M., Vasiliev S. A., Frolov A. A., Medvedkov O. I., Rybaltovskii A. O., and Titova V. A., "Hydrogen enhancement of near-UV photosensitivity of germanosilicate glass," SPIE Proc. 2998, pp. 111-121 (1997). 130 Starodubov D. S., Grubsky V., Feinberg J., and Erdogan T., "Near-UV fabrication of ultrastrong Bragg gratings in hydrogen loaded germanosilicate fibers," Proc. of CLEO'97, post-deadline paper CDP24, 1997. 131 Patrick H. J., Askins C. G., McElhanon R. W. and Friebele E. J. Electron. Lett., 33(13), 1167-1168, 19 June 1997.

Chapter

4

Theory of Fiber Bragg Gratings

Wave propagation in optical fibers is analyzed by solving Maxwelrs equations with appropriate boundary conditions. The problem of finding solutions to the wave-propagation equations is simplified by assuming weak guidance, which allows the decomposition of the modes into an orthogonal set of transversely polarized modes [1-3]. The solutions provide the basic field distributions of the bound and radiation modes of the waveguide. These modes propagate without coupling in the absence of any perturbation (e.g., bend). Coupling of specific propagating modes can occur if the waveguide has a phase and/or amplitude perturbation that is periodic with a perturbation "phase/amplitude-constant" close to the sum or difference between the propagation constants of the modes. The technique normally applied for solving this type of a problem is coupled-mode theory [4-9]. The method assumes that the mode fields of the unperturbed waveguide remain unchanged in the presence of weak perturbation. This approach provides a set of first-order differential equations for the change in the amplitude of the fields along the fiber, which have analytical solutions for uniform sinusoidal periodic perturbations. A fiber Bragg grating of a constant refractive index modulation and period therefore has an analytical solution. A complex grating may be considered to be a concatenation of several small sections, each of constant period and unique refractive index modulation. Thus, the modeling of the transfer characteristics of fiber Bragg gratings becomes a relatively simple 119

120

Chapter 4

Theory of Fiber Bragg Gratings

matter, and the application of the transfer matrix method [10] provides a clear and fast technique for analyzing more complex structures. Another technique for solving the transfer function of fiber Bragg gratings is by the application of a scheme proposed by Rouard [11] for a multilayer dielectric thin film and applied by Weller-Brophy and Hall [12,13]. The method relies on the calculation of the reflected and transmitted fields at an interface between two dielectric slabs of dissimilar refractive indexes. Its equivalent reflectivity and phase then replace the slab. Using a matrix method, the reflection and phase response of a single period may be evaluated. Alternatively, using the analytical solution of a grating with a uniform period and refractive index modulation as in the previous method, the field reflection and transmission coefficients of a single period may be used instead. However, the thin-film approach does allow a refractive index modulation of arbitrary shape (not necessarily sinusoidal, but triangular or other) to be modeled with ease and can handle effects of saturation of the refractive index modulation. The disadvantage of Rouard's technique is the long computation time and the limited dynamic range owing to rounding errors. The Bloch theory [14,15] approach, which results in the exact eigenmode solutions of periodic structures, has been used to analyze complex gratings [16] as well. This approach can lead to a deeper physical insight into the dispersion characteristics of gratings. A more recent approach taken by Peral et al. [ 17] has been to develop the Gel'Fand-Levitan-Marchenko coupled integral equations [18] to exactly solve the inverse scattering problem for the design of a desired filter. Peral et al. have combined the attributes of the Fourier transform technique [19,20] (useful for low reflection coefficients, since it does not take account of resonance effects within the grating), the local reflection method [21], and optimization of the inverse scattering problem [22,23] to present a new method that allows the design of gratings with required features in both phase and reflection. The method has been recently applied to fabricate near "top-hat" reflectivity filters with low dispersion [24]. Other theoretical tools such as the effective index method [25], useful for planar waveguide applications, discrete-time [26], Hamiltonian [27], and variational [28], are recommended to the interested reader. For nonlinear gratings, the generalized matrix approach [29] has also been used. For ultrastrong gratings, the matrix method can be modified to avoid the problems of the slowly varying approximation [30].

4.1

121

Wave Propagation

The straightforward transfer matrix method provides high accuracy for modeling in the frequency domain. Many representative varieties of the types and physical forms of practically realizable gratings may be analyzed in this way.

4.1

Wave Propagation

The theory of fiber Bragg gratings may be developed by considering the propagation of modes in an optical fiber. Although guided wave optics is well established, the relationship between the mode and the refractive index perturbation in a Bragg grating plays an important role on the overall efficiency and type of scattering allowed by the symmetry of the problem. Here, wave-propagation in optical fiber is introduced, followed by the theory of mode coupling. We begin with the constitutive relations D = SoE + P

(4.1.1)

B = teoH

(4.1.2)

where So is the dielectric constant and tt o is the magnetic permeability, both scalar quantities; D is the electric displacement vector; E is the applied electric; B and H are the magnetic flux and field vectors, respectively; and P is the induced polarization, = SoX~/(1)E.

(4.1.3)

The linear susceptibility X~](1) is in general a second-rank tensor with two laboratory frame polarization subscripts ij and is related to the permittivity tensor sij with similar subscripts as si/ = 1 + X/j (1).

(4.1.4)

Assuming that the dielectric waveguide is source free, so t h a t V - D = 0,

(4.1.5)

and in the absence of ferromagnetic materials, V-B=0,

(4.1.6)

122

Chapter 4

Theory of Fiber Bragg Gratings

the electric field described in complex notation is -- = -~ 1 [Ee i ( ' t - ~z) + Ee_i(~_~z)] ' E

(4.1.7)

and the induced polarization vector is also similarly defined. Using Maxwell's equations, V xE=

OB

(4.1.8)

Ot

(4.1.9)

V x H = OD + 3, Ot

where J is the displacement current, and using Eq. (4.1.1) in Eq. (4.1.9) and with J = 0, we get -

(4.1.10)

VXH=o- ~

Taking the curl of Eq. (4.1.8) and using Eqs. (4.1.2)-(4.1.5) and the time derivative of Eq. (4.1.10), the wave equation is easily shown to be 632E

02P

V2Lv =/z~1760--~ + /z~ at 2"

(4.1.11)

Using Eq. (4.1.3) and (4.1.4) in (4.1.11), we arrive at 02 V2Lv =/Zoe o ~-~ [ 1 + Xo.(1)]~'~,

(4.1.12)

or V2E-

4.1.1

/.toSoSi j

02E Ot2"

(4.1.13)

Waveguides

The next step in the analysis is to introduce guided modes of the optical fiber into the wave equation. The modes of an optical fiber can be described as a summation ofl transverse guided mode amplitudes, A~(z), along with a continuum of radiation modes, Ap(z)[2], with corresponding propagation constant, fl/~ and tip, 1 /z=l E t -

-~

E

/1=1

p=oo

+ cc3 + E f

p=O

,:;,o, (4.1.14)

4.1 WavePropagation

123

where ~ t and ~ are the radial transverse field distributions of the ttth guided and pth radiation modes, respectively. Here the polarization of the fields has been implicitly included in the transverse subscript, t. The summation before the integral in Eq. (4.1.14) is a reminder t h a t all the different types of radiation modes must also be accounted for [e.g., transverse electric (TE) and transverse magnetic (TM), as well as the hybrid (EH and HE) modes]. The following orthogonality relationship ensures that the power carried in the ttth mode in watts is ~ i 2 : ~z "[~t X ~vt]dxdy = 1/2

1/2 co

~t" ~vt dxdy = 8~v.

flit

co

co

co

(4.1.15) Here, ez is a unit vector along the propagation direction z. ~ v is Kronecker's delta and is unity for tt = v, but zero otherwise. Note t h a t this result is identical to integrating Poynting's vector (power-flow density) for the mode field transversely across the waveguide. In the case of radiation modes, ~ v is the Dirac delta function which is infinite for tt = v and zero for t t r v. Equation (4.1.15) applies to the weakly guiding case for which the longitudinal component of the electric field is much smaller t h a n the transverse component, rendering the modes predominantly linearly polarized in the transverse direction to the direction of propagation [1]. Hence, the transverse component of the magnetic field is Ht =

tto

X

(4.1.16)

The fields satisfy the wave equation (4.1.13) as well as being bounded by the waveguide. The mode fields in the core are J-Bessel functions and K-Bessel functions in the cladding of a cylindrical waveguide. In the general case, the solutions are two sets of orthogonally polarized modes. The transverse fields for the ttth x-polarized mode t h a t satisfy the wave equation (4.1.13) are then given by [2]

~x= C ~ J ~ ( u r ) ~ c ~

/-/,= nelr

(4.1.17)

(4.1.18)

124

Chapter 4

Theory of Fiber Bragg Gratings

and the corresponding fields in the cladding are

( r){co

Hy = neff

(4.1.19)

sin ttr

~x = C~ K ~ ( w ) K ~ w

(4.1.20)

~x,

where the following normalized parameters have been used in Eqs. (4.1.17)-(4.1.20): v --

u--

27ra

27ra

~ / n c2re

--

n c l2a d

(4.1.21)

- - n c2re

- n e2ff

(4.1.22)

w 2 = v 2 - u 2,

(4.1.23)

and

nc a [ (nc~ = nc a ) + \

nclad

/

1]

(4.1.24)

'

where neff is the effective index of the mode and w2

b = ~-~.

(4.1.25)

Finally, assuming only a single polarization, the y-polarized mode, ~y = H x = O.

(4.1.26)

The choice of the cosine or the sine term for the modes is somewhat arbitrary for perfectly circular nonbirefringent fibers. These sets of modes become degenerate. Since the power carried in the mode in watts is ~4~12, from the Poynting's vector relationship of Eq. (4.1.15), the normalization constant C~ can be expressed as

2w [ V.~o 11~ C~- av neff~e~l~_l-~))j~+l(U)lj ,

(4.1.27)

4.2

125

Coupled-mode theory

where e~ = 2 when tt = 0 (fundamental mode) and 1 for tt r 0. Matching the fields at the core-cladding boundary results in the waveguide characteristic eigenvalue equation, which may be solved to calculate the propagation constants of the modes: u

4.2

J.+l(U) = J~(u)

w

g.+l(w) g~(w)

"

(4.1.28)

Coupled-mode theory

The waveguide modes satisfy the unperturbed wave equation (4.1.13) and have solutions described in Eqs. (4.1.17) through (4.1.20). In order to derive the coupled mode equations, effects of perturbation have to be included, assuming that the modes of the unperturbed waveguide remain unchanged. We begin with the wave equation (4.1.11) 02Lv 02P V2Lv = ttoS o ~ + tLo Ot2"

(4.2.1)

Assuming that wave propagation takes place in a perturbed system with a dielectric grating, the total polarization response of the dielectric medium described in Eq. (4.2.1) can be separated into two terms, unperturbed and the perturbed polarization, as m

P

m

= Punpert + Pgrating,

(4.2.2)

where

Punpert--

t~o)~l)E/~ 9

(4.2.3)

Equation (4.2.1) thus becomes,

V2EtLt =

02

02

/'Lo~o~r ~ El.it + /-tO - ~ Pgrating,~,

(4.2.4)

where the subscripts refer to the transverse mode number tL. For the present, the nature of the perturbed polarization, which is driven by the propagating electric field and is due to the presence of the grating, is a detail which will be included later.

Chapter 4 Theory of Fiber Bragg Gratings

126

Substituting the modes in Eq. (4.1.14) into (4.2.4) provides the following relationship: V2

~ [AtL(z)~t ei(~t-t~'z) + cc] + ~ /1,=1

Ao(z)~ptei(~-t~pz) dp p=0

-- ]ttOF~OF'r-~

[At~(z)~tLtei(~-t~'z) + cc] + ~

E

P=~176

~=1

p=O

02 -- ]LtO- ~ Pgrating,lt"

(4.2.5)

Ignoring coupling to the radiation modes for the moment allows the left-hand side of Eq. (4.1.13) to be expanded. In weak coupling, further simplification is possible by applying the slowly varying envelope approximation (SVEA). This requires that the amplitude of the mode change slowly over a distance of the wavelength of the light as

02At~ 0Z 2

OAt~ > Ag, the electric field for the f u n d a m e n t a l mode decays approximately as it would for constant a t t e n u a t i o n per unit length. The attenuation constant depends on wavelength and the transverse distribution of the grating and the incident field, but not on z. This approximate result suggests t h a t the filter loss spectrum should be independent of the length of the grating, which is indeed the case. To calculate the scattered power and the spectrum of the radiation, we use Eq. (4.7.6) in Eq. (4.7.5) and include the grating function Wgrating to arrive at

Escatter(R,~b,~p ) _. -R r ffwg rating(X~)Eo(x~)eif~clad(-X

cos ~bsin q~-y sin C s i n q~)

(4.7.11) • IL(X,Lg)dxdy,

where Lg is the length of the fiber grating, the constant F is given F

=

[3cladAneiflcladR

(4.7.12)

and IL(X, Lg) is obtained by integration with respect to z, -

In(xVLg)

e iyx e (iAflb-~ 2 iAflb-

- 1 a

§

e -iyx e (iyflf-~ 2 iAflf-

- 1 , a

(4.7.13)

where 7 was defined in (4.7.2), and hflf and hflb are the forward and b a c k w a r d phase mismatch factors,

A~

"- /3f-Jr ~clad

2 Ir cos 0r COS ( f l -

(4.7.14)

A/3f = /3f + [3clad

2 ~r cos 0r COS q~ +

where [~clad = 2 7Tnclad//~, and the signs are consistent with the measurement of the angle, ~. The forward scattering process can easily be included

4.7 Radiationmodecouplers

165

if necessary but is ignored for now. For the b a c k w a r d phase-matching condition, the radiation angle at resonance, ~L, is given by the Aflf = 0, as has been seen in Section 4.2.5, so t h a t

~f + ~clad COS q ~ L

--

2 7r cos Og/Ag.

(4.7.15)

The last result is a longitudinal phase-matching condition, which is exactly the same as normal Bragg reflection. It requires t h a t the path difference between light scattered from points t h a t are both on a line parallel to the optical axis of the fiber, and on adjacent fringes of the grating, should be exactly A (Fig. 4.18). Ignoring the forward scatter, we find the scattered counterpropagating power from Eqs. (4.7.11), (4.7.3), and (4.7.4) as 1

escatter(/~) - ~ nclad X f

27r

r

f

7r

r

F*Fe -~L

(4.7.16)

Ilcore(%q~,~b)l2 sinh2(~L/2) + sin2(AflbL/2) hfl~ + a 2

sin ? d~ de,

where the overlap integral over the profile of the grating, which we refer to as the transverse phase-matching condition, is

Icore( T,q~,r

__ f ~ Wgrating(X~)Eo(x~)ei[X(T-~cladCOS JJ

(4.7.17) ~bsin

(P)--[3cladYs i n ~bsin ~]dxdy.

F i g u r e 4 . 1 8 : Scattered light from the fringe planes of the gratings adds up in phase when the resonance condition for longitudinal phase matching is met. AB § BC = NA, at resonance.

Chapter 4 Theory of Fiber Bragg Gratings

166

In u n d e r s t a n d i n g the physics of the scattering, we consider separately the two components of the integral, the transverse phase-matching term (Eq. 4.7.17) and the longitudinal phase-matching (pm) t e r m which depends on the detuning, Aflb. In the low-loss regime (a < hflb), the longitudinal pm term is simply like the Bragg matched reflection condition, but now as a function of ~. For all practical purposes, this term is like a delta function t h a t is only significant at very small angles of radiation (~ < 1~ The integral has a t e r m dependent on cos~, which becomes broader and asymmetric in its a n g u l a r b a n d w i d t h as ~ ~ 0 ~ and which is also inversely dependent on the length of the grating. For typical filter lengths of a few millimeters, we find the a n g u l a r b a n d w i d t h to be - 1 ~ The a s y m m e t r y and broadening at small phase-matching angles have been observed in phase-matched second-harmonic generation with periodic structures [50]. In the high-loss regime, we find t h a t the delta function broadens but has a width similar to t h a t of the low-loss case. We can therefore choose to consider the dependence of the scattered power on the longitudinal phase matching as a very narrow filter at a given angle. Comparison of the longitudinal term with the transverse pm condition of Eq. (4.7.17) shows t h a t the a n g u l a r dependence of the radiation for the transverse case varies much more slowly and m a y be approximated to be a constant over the region of the longitudinal bandwidth. Figure 4.19 shows the dependence of the longitudinal and the transverse pm as a comparison for s t a n d a r d fiber and a uniform grating profile, Wgrating - 1. The longitudinal response for a blaze angle of 5 ~ and the transverse response for three blaze angles are shown. The analytical result for the loss coefficient a has been shown to be [51],

k2a2~cladAn2

r

Ilcore( % qP~r 2d r rE2(r)dr

32 r 2 r=0

By normalizing the radius as p = r / a (a is the core radius), oo

~

I +2 m= Zl

7rk2a2~clad An2 foo 4

r=O

pE2( p)dp ,

(4.7.19)

4.7 Radiationmodecouplers 1.2

167

'

1.0

0 dB filter loss

.'f'~l

Q - 0 8

0

|__

40 dB

.-'-")I

-o 0.6

N 0.4 E

- - 2 0 dB '

._

,_

li', \'~ \

" 0.2 O

-

Z

.

0.0

.

.

_

.

J/

. . . _

9.8

10.0 Output angle, (1) (degrees)

10.2

Blaze Angle

1,0

"

o-0.8

-

/

0

"o0.6

~

/

-

~0.4 -

e

~

/

|

"~\

/

,'" -"

.~,.............. 9 99

~

9

4 degrees 6 degrees 8 degrees

9 ..

,

*

:,.~ --

"~176

.

/

z 0.2 0.0-

-

J

9 ...........

0

I . . . . . . . . . . .

2

'

......... -'"

-"

4

.o *" ~ ~ o.~176

".,, ~

~ ~

6 8 10 12 14 Output angle, (P (degrees)

16

18

F i g u r e 4 . 1 9 : (a) shows the longitudinal integral and (b) is the transverse integral for different blaze angles. and Eo(p) is the field distribution of t h e f u n d a m e n t a l mode. The i n t e g r a l s I o and I m are defined as

Io : I ~

JR =o Wgrat(p)Eo(P)Jo( ypa)Jo((Lp a)pdp

Im -- Jr=l--oWgrat(p)E~

(4.7.20)

( ypa )dm ( (Lpa )fldP"

In Eq. (4.7.20), we r e m i n d ourselves t h a t y is t h e t r a n s v e r s e g r a t i n g m o m e n t u m t h a t allows the mode to couple out of t h e core a n d is a function of the g r a t i n g period as well as the blaze angle, Y=

2~r sin 0g Ag "

(4.7.21)

Chapter 4 Theory of Fiber Bragg Gratings

168

~L is the transverse momentum of the mode, depending on the output radiation angle of the scattered light, ~PL, at a given wavelength, and is

~L = ~cladsin q~L"

(4.7.22)

In Fig. 4.20 is shown the calculated and measured loss spectrum of fibers with nominally the same v-value, but different core radii. The agreement between the measured loss and the calculated loss spectrum is quite good for two fibers. The blaze angle for the grating is 8 ~. The results also show t h a t the loss spectrum due to scattering into the radiation modes is independent of the fiber length, and, indeed, this has been confirmed by experimental observations [51]. The reflection coupling constant for a tilted grating [38] with an arbitrary profile is

f ~=oPWgrating(P)Jo(2 ~- a sin Ogp/A)E2(p)dp ---

foo pE2(p)dp

Kac oc

9

(4.7.23)

p=O This integral has been plotted in Fig. 4.21 and shows that zero Bragg reflection into the guided mode occurs at a lower blaze angle if the grating is moved outward from the core. For comparison, the back reflection from two fibers has been shown, one with a grating situated entirely in the cladding and the other with a standard telecommunications fiber core.

101

0.9 0.8

0.7 __o 0.6 10.5 "-4:~ l/

Theory: core dia = 7 urn. ....... core d i a = . . . . . - - ' " core d i a = 12 um -~ . . . . Rad. Loss M e a s 1. ~ ~

~ 0.3 nr" 0"4 I

--

0.2 0.1 0.0

1510

~- :. ~ ."# ."l" .."~"~

9 trn

Measurement 2

~

~, :. "~t '', iriS; ".

~,..~.~_.....

I~'~"'~

........

~ 1520

1530

1540

1550

1560

1570

1580

1590

W a v e l e n g t h , nm

F i g u r e 4.20: Measured radiation loss from large core weakly guiding fibers with radii of 7, 9, and 12 microns and a v-value of 1.9. Two measurements on 12micron core-diameter fibers are also shown (after Ref. [52]).

4. 7

169

Radiation mode couplers

O _

111 -o

v

standard telecommunication fiber photosensitive cladding

\\

c -20

o o G) m

\\

.m

\9

j

l J

l

/

! .

o

n" -40

. .

'i

o

I: 11

rn

ili/

-60 0

2

4 6 8 Writing angle (degrees)

10

12

F i g u r e 4 . 2 1 - Comparison of back reflection from two fibers: both have nominally the same v-values, but one has a photosensitive cladding only (after Ref. [52]).

We note t h a t the first back reflection m i n i m u m occurs at - 3 ~ external writing angle for the photosensitive cladding fiber, compared with 8 ~ for the s t a n d a r d fiber. This has an additional benefit of reducing the bandwidth over which radiation loss occurs, as seen from the phase-matching diagram in Section 4.2.5. In Fig. 4.22 is shown the filter response for coupling to radiation modes for the photosensitive cladding fiber. The benefit of m a k i n g the cladding photosensitive is clear, since it reduces the b a n d w i d t h at the zero reflection writing angle (measured at 3 ~ and calculated for the fiber to be -~3.6~ The core radius of this fiber is 3.4 ttm, and the photosensitive cladding extends from a to 4a. The a g r e e m e n t between the theoretical and experimentally observed properties of tilted fiber Bragg gratings is extremely good [38] using the complete theory presented by Erdogan [40,38]. In particular, the m e a s u r e d peak visible at 1545 n m in Fig. 4.22 is shown to be due to leaky mode coupling. The polarization dependence of tilted Bragg gratings in fibers with a core radius o f - 2 . 6 ttm and a core-to-cladding refractive index difference of 5.5 • 10 -3 becomes obvious as the tilt angle exceeds 6.5 ~ [38]. Above this angle, the p-polarization scatters less efficiently t h a n the s-polarization. Below a tilt angle of 6.5 ~ the radiation loss is predominantly due to coupling to even-azimuthal order radiation modes, giving

170

Chapter 4 1.520

1.515

12

I

10 -

"

"a

8 -

"

0 --J

6

Lr.

4

en

....

1.525

1.530

1.535

1.540

1.550

1.545

1.555

i Filter response (dB), 4um 3.4 deg calculated I

3.0 deg,' measu red ~ "\" ~ ' ,

~'///~ ~ ' i

.-- -- Filter response ( d B ) , ~ . 3.4um/3.6 deg, calculated ~

""

Theory of Fiber Bragg Gratings

"

~

wavelength,

;l-y

!

um

F i g u r e 4.22: The loss spectrum (calculated and measured) for a photosensitive cladding fiber. The ripple in the loss spectra is a measurement artifact (after Ref. [52]). rise to a sharp narrow-bandwidth peak. Above 6.5 ~ the coupling is to oddazimuthal order modes and becomes much broader. By m a k i n g angles for the back-reflection small (Fig. 4.21), one benefits from both low polarization sensitivity and a narrow-loss spectrum. In Fig. 4.23 is shown the design diagram for STG filters as a function of the core-to-cladding refractive index difference, assuming an infinite

9

45 V

40

,,,,s"

1.6 ~

35 E ~" 30

~.~,,.-."~ .....

25

-

8

-

7

-

6

- 5~. {3)

"0

~" 20

-

4

30 dB is necessary. This requirement immediately points to a EL > 4.16. Therefore, this filter may not be an ideal candidate, since both requirements may be difficult to achieve. Fiber Bragg gratings with multiple phase-shifted sections have been realized for band-pass applications. Bhakti and Sansonetti [ 13] have modeled the response of gratings with up to eight phase-shifted sections. The design strategy was for an optimized band-pass filter with a - 0 . 8 - n m bandwidth, as well as negligible in-band ripple. Increasing the number of sections was shown to make the pass band more rectangular, but reduced the stopped bandwidth. An asymptotic value for the band-stop bandwidth is approached with greater t h a n 5 phase shifts and is twice the pass bandwidth. This is another severe limitation on the use of such filters. Phase masks with the appropriate quarter-wavelength shifts [6] were used to replicate a three-phase-shift grating. With careful UV illumination, the band pass was fully resolved and showed excellent agreement with theory [13]. The band-pass/stop widths were 0.88 nm/2.77 nm with a peak rejection of 13 dB. The optimized grating length were L1 = L4 = 0.22 mm and L 2 - L 3 - 0.502 mm, with a refractive index modulation amplitude of 1.5 • 1 0 - 3 .

6.1 Distributed feedback, Fabry-Perot, superstructure, and moird gratings

237

While the principle of multiple phase shift within a single grating is useful, it has the additional effect of increasing the side-lobe structure despite apodization. The side lobes increase as a result of the formation of a super structure (see C h a p t e r 3) and is discussed in the next section. Other methods need to be used to position the band pass and for a broaderbandwidth band pass and more controllable b a n d w i d t h of the band stop. A simple technique to accurately create a band pass at a particular wavelength is to introduce a phase step within a chirped grating. A s t a r t and a stop Bragg wavelength characterize a chirped grating. In a linearly chirped grating, the position of the local Bragg wavelength is uniquely known. Placing a 17"/2phase step at t h a t point results in a band pass at the local Bragg wavelength. Figure 6.8 shows the t r a n s m i t t e d spectrum of two 10-mm-long gratings. Data A and B refer to the same spectrum, with B displayed on a 30 times expanded wavelength scale. A shows the effect of a single quarterwavelength phase step in the center, while C shows the step at one-third the distance from the long-wavelength end of the grating. The effect of the stitch is localized in the reflected spectrum, and several more bandpass structures may be placed within this grating. For example, a bandpass every 2 n m is easily achieved. However, the effects of the super

1.0

!

0.8 ,-- 0.6 .o oo ._m 0.4 E " 0.2 I-'-

0.0 1535

I

i i

I ,

i

........... 1540

l*-c

1 ""'"':A/~

1545

1550

.......

1555

...............

1560

1565

Wavelength, nm

F i g u r e 6.8: The transmission spectrum of a grating with a single ~r/2 phase step in the center of a chirped bandwidth of 20 nm (A). An • expanded view of the band-pass spectrum is also shown (B). Also shown is the effect of placing the phase step at 2/3Lg (C); the band-pass peak shifts to the local Bragg wavelength. The grating is 10 mm long.

238

Chapter 6 Fiber Grating Band-pass Filters

structure become a p p a r e n t in t h a t additional peaks appear and the bandpass spectrum acquires side lobes. A 10-mm-long grating transmission spectrum with 20 phase steps is shown in Fig. 6.9. Note t h a t within the pass band of the grating there is a small associated dispersion since the grating is chirped. Since the gratings are used as a band-pass, r a t h e r t h a n in reflection, dispersion is less of an issue, other t h a n at the band edges. Apodization only helps slightly; it also reduces the bandwidth and the extinction at the edges of the grating, so t h a t it is of limited value. Blanking-off part of a chirped grating during fabrication instead of introducing phase steps is an effective way of creating a band-pass filter [14]. The net result is t h a t p a r t of the chirped grating is not replicated, thus opening a band gap. This principle is effective for a narrow-bandwidth band pass (1 nm) so long as EL < ~r. With a stronger reflectivity grating, the b a n d w i d t h of the band stop increases to encroach on the band pass from both sides, reducing the pass-band width. An alternative technique uses UV postprocessing first reported for UV t r i m m i n g of the refractive index of photosensitive waveguides [53], to erase part of the chirped grating written in a fiber [15]. In order to fabricate a single band pass within a broad stop band (>50 nm), several chirped gratings may be concatenated along side a chirped grating with the band gap. With care and choice of chirped gratings, single and multiple band-pass filters

0

-10

'

"~,

-!

ti

{

r

v', .... ~i

:',

;

i~

:~

;

tYI

I

"O

E-20

~

0

|~|

"._

~.-40

~i I

v.

'

'

1540

.,~

;';

;'.

,

'i

I

,~

~"'

':'

'

"

.'

::

:

:i

''

i;

~.r

1550 Wavelength,

; J,

!ii: 1555

:'i~

.'. i~

:',

,'

..... u.;~ 1545

.~

::

i ! ! f : =,

~ 1535

~

t

'

,; :

"

; ! ~:

;

, ';

.~ 1560

1565

nm

F i g u r e 6.9: A 20 • r phase-step grating band-pass filter. Each band pass has an extinction of >30 dB, but with some side-lobe structure at - 1 5 dB. Ghosts appear between the main pass bands as a result of the super structure of phase steps at -30 dB transmission.

6.1

Distributed feedback, Fabry-Perot, superstructure, and moird gratings

239

have been successfully demonstrated, with a pass/stop-bandwidth of 0.17 n m / l l . 3 n m and extinction o f - 10 dB. A four-channel filter evenly spaced over a stop bandwidth of 50 n m has also been reported [15]. Insertion loss of these types of chirped filters is a problem, since radiation loss on the blue-wavelength side affects the m a x i m u m transmission of the pass band. As a consequence of large KL and radiation loss, a m a x i m u m transmission o f - 7 5 % was reported for these band-pass filters. Broader pass-bandwidth filters may be fabricated by the use of concatenated chirped gratings [16]. The effects of "in-filling" due to the use of large rJ~ values are diminished by increasing the band-pass width. The arrangement for such a filter allows better extinction in the stop band (>30 dB) while permitting the placement of the bandpass at the required wavelength. Additionally, chirped gratings show reasonably smooth stop band edges. Concatenating two such gratings with a nonoverlapping band stop results in a band pass between the two band-stop regions. While this scheme has been applied to chirped gratings, Mizrahi et al. [17] have shown that two concatenated highly reflective gratings with a pass band in between the Bragg wavelengths can be used as a band-pass filter. Radiation loss within the pass band are avoided by using a strongly guiding fiber, which further blue-shifts the radiation loss spectrum from the long-wavelength stop band. The bandwidth of the pass band was - 1 . 6 nm with an extinction in excess of 50 dB and a stop band o f - 6 nm.

6.1.2

Superstructure band-pass filter

It has been shown t h a t placing more t h a n a single M4 phase step within the grating results in as many band-pass peaks appearing within the band stop [12]. This principle may be extended to produce the superstructure grating [18,22], but works in reflection. The reflection spectrum has several narrow-bandwidth reflection peaks. The principle has been used in semiconductor lasers to allow step tuning of lasers. However, a badly stitched phase mask will produce similar results. Since a phase m a s k is generally manufactured by stitching small grating fields together, errors arise if the fields are not positioned correctly. These random "phase errors" are like multiple phase shifts within the grating, resulting in multiple reflection peaks, each with bandwidth inversely proportional to the overall length of the grating, and spaced at wavelength intervals inversely pro-

240

Chapter 6 Fiber Grating Band-pass Filters

portional to the length of the field size (see Chapter 3). Figure 6.10 shows the super structure on a 30-mm-long grating reproduced from a phase mask with stitching errors. Despite these errors, the grating reflection and phase response for the main peak are very close to being theoretically perfect [19]. The theory of superstructure gratings is discussed in Chapter 3. For filter applications, it is necessary to achieve the appropriate characteristics. Here we consider the spectra of short superstructure gratings, which may be conveniently fabricated with an appropriate phase mask. Figure 6.11 shows the reflection and transmission characteristics of a superstructure grating, comprising 11 • 0.182 mm long gratings, each separated by 1.555 mm. The overall envelope of the transmission spectrum (see Fig. 6.11b) has been shown in Chapter 3 to be governed by the bandwidth of the subgrating. Note in Fig. 6.11a t h a t the bandwidth of the adjacent peaks becomes smaller. This is a function of the reflectivity at the edges of the grating. In order to use this filter as a band-pass filter, it is necessary to invert its reflection spectrum. This may be done by using a fiber coupler. However, the input signal is split into two at the coupler. One half is reflected from the grating and suffers another 3-dB loss penalty in traversing the

Reflection Spectrum of 30mm Long Grating With Stitching Errors 0

1.547

1.548

1.548

1.549

1.55

1.549

-5 -10

A.

-15 -20

~:~ - 2 5 -30

i

-35 -40

I "'

,JTIl/v lf*7/[I v l'v

I' tllt/Vll/Afll v V'lll/IU

n

V

..................

Wavelength, microns

F i g u r e 6.10: Reflection spectrum of superstructure grating. The disadvantage of the superstructure grating--the reflection coefficient cannot be made the same for each reflection [29]. This limitation can be overcome by using a different type of moir~ grating [20], which has been discussed in Chapter 3.

6.1

Distributed feedback, Fabry-Perot, superstructure, and moirg gratings

1550

1552

1554

1556

1558

I

0

241

1560

I

-5--

~

-10 -

-15

a)

Wavelength, nm 1550

rn "o o

o

1554

1556

1558

0 -5

-

c" -10 ~

1552

-15 -

_

E -20 -

_

;.i

i:

i

"

i

"i

:'

"

1560

/

!l

'- -25 I - -30

b)

Wavelength, nm

6.11: (a) The reflectivity spectrum of a superstructure grating with 9 • 222 micron grating sections separated by l-ram gaps. Refractive index modulation amplitude is 10 -3. (b) The transmission spectrum of the grating shown in (a). Also shown is the transmission spectrum of a single section of the grating of 0.181 microns long. The envelope has been normalized to fit the superstructure spectra.

Figure

coupler once again. The reflected spectrum is therefore - 6 dB relative to the input signal. A fiber circulator overcomes this loss penalty [21]. The insertion loss of a circulator is approximately 1 dB, so t h a t an efficient multiple band-pass filter can be fabricated. In an interesting demonstration, a chirped superstructure grating has been used for multiple-channel dispersion compensation, since the repeat band stops have a near-identical chirp [22]. The advantage of such a scheme is t h a t it requires only a single temperature-stabilized grating to equalize several channels simultaneously, although the reflection coefficient varies for each reflection.

242

6.2

Chapter 6 Fiber Grating Band-pass Filters

The Fabry-Perot filters

a n d moir

band-pass

The fiber DFB grating is the simplest type of Fabry-Perot (FP) filter. Increasing the gap between the two grating sections enables multiple band-pass peaks to appear within the stop band. The bandwidth and the reflectivity of the gratings determine the free-spectral range and the finesse of the FP filter. The grating FP filter has been theoretically analyzed by Legoubin et al. [23]. Equations (6.1.4) and (6.1.5) describe the transfer characteristics of the filter and have been used in the simulation of the gratings in this section. Figure 6.12 shows the structure of a Fabry-Perot filter. These filters work in the same way as bulk FP interferometers, except that the gratings are narrow-band and are distributed reflectors. A broader bandwidth achieved with chirped gratings creates several band-pass peaks within the stop band. Control of the grating length L and the separation ~/allows easy alteration of the stop-band and the free-spectral range. At zero detuning, the peak reflectivity of a FP filter with identical Bragg gratings is RFp-

4R (1 + R) 2'

(6.2.1)

where R is the peak reflectivity of each grating. Since the gratings are not point reflectors, the free-spectral range (FSR) is a function of the effective length of the grating, which in t u r n is dependent on the detuning. For a bulk FP interferometer, e.g., a fiber with mirrors, the FSR is [23] FSR =

1 2dneff(A)"

(6.2.2)

The distance between the mirrors is d, and the effective index of the mode

Figure 6.12: A schematic ofa Fabry-Perot etalon filter. In the simple configuration, the gratings are identical, although in a more complicated band-pass filter, a dissimilar chirped grating may be used.

6.2

243

The Fabry-Perot and moird band-pass filters

neff is a function of wavelength. For an equivalent fiber-grating-based FP

interferometer, the thickness d becomes a function of wavelength, and only at the peak reflectance is the FSR largest. The effective thickness is the separation between the inner edges of the gratings plus twice the effective length of the gratings. Off resonance, the penetration into the grating is greater t h a n on-resonance, leading to a bigger thickness. Therefore, at the edges of the FP bandwidth, the FSR becomes smaller. The first in-fiber grating FP filter was reported by Huber [24]. A transmission bandwidth of 29 pm was reported. F u r t h e r multi-band-pass in-fiber FP resonators have also been demonstrated [25]. In the latter report, a 100-mm-long FP interferometer was fabricated with two 95.5% reflecting gratings. A finesse of 67 was achieved with the free spectral range of i GHz and a pass bandwidth of 15 MHz. In order to measure the transmission spectrum of the FP, a piezoelectric stretcher was used to scan the fiber etalon in conjunction with a fixed frequency DFB laser source operating within the bandwidth of the grating band stop, at a wavelength of 1299 nm. A peak transmission of - 8 6 % of the fringe maxim u m was also noted. Figure 6.13 shows the transmission characteristics of a FP filter made with two gratings, each 0.5 mm long with a 5 mm separation and a refractive index modulation of 2 x 10 -4. The weak ripple within the band-stop of the filter is due to the poor finesse of the FP but is ideal in WDM transmission to control solitons. The shortest gratings

1.0 0.8

T T T T TT

-

,.-- 0 . 6 0

._~ 0.4 E oo c 0.2I--

0.0 1550.0

I

I

I

1551.0

1552.0

1553.0

1554.0

Wavelength, nm

F i g u r e 6 . 1 3 : A FP filter with a 5-mm gap. Grating lengths are 0.5 mm with index modulation of 2 x 10 -4. The arrows show where WDM channels may be placed within the band-pass filter for soliton guiding.

244

Chapter 6 Fiber Grating Band-pass Filters

in a FP filter reported to date are ~0.3 m m long, separated by a similar distance [26]. The resulting multiple band pass, which was a shallow ripple of ~50% transmission was used as a guiding filter in wavelength division multiplexed soliton transmission experiments to suppress Gord o n - H a u s jitter [27]. With stronger gratings, multiple band-pass filters with deeper band stops are easily possible. However, even slight loss in the grating (absorption due to O H - ions) can degrade the transmission peaks substantially. It is therefore advantageous to use deuterated fiber for this type of a filter. Figure 6.14 demonstrates a 4-mm-long grating with a gap of 5 mm in the center. This filter shows ~30-dB extinction in the center of the band pass. Note t h a t all these filters have a similar narrow band-pass response t h a t plagues the highly reflecting DFB grating filter. Thus, applications for such a grating are likely to be in areas in which either high extinction or high finesse, or low extinction and large bandwidth are required. Figure 6.15 shows the m e a s u r e d transmission of a 0.6-mm-long FP filter with a 2.5-mm gap. The pass bands have been m e a s u r e d with a resolution of 0.1 n m and are therefore not fully resolved. The structure should be deeper and much narrower. Nevertheless, the dips in transfer characteristics match the theoretical simulation extremely well with the parameters shown. Typically, the best results for band-pass peaks for this type of FP filter, using either chirped or unchirped gratings with an extinction of 30 dB, is ~70%.

1551.0 0 -5

133 "o9 - 1 0

..--

1551.5 -v

1552.5

1552.0

V-,_..-I

i_..._~V

1553.0 _.._...-

__._.

--

--

._o - 1 5

--

~9 - 2 0

--

r

-25

--

,-

-30 Wavelength,

nm

F i g u r e 6.14: A 4-mm-long grating FP filter with a 5-mm gap and a An of 5 X 10 -4.

6.2

245

The Fabry-Perot and moird band-pass filters

1.545 -45

1.547

1.549

1.551

1.553

1.555

/

-50

"~ -55 d -60 r~

O oH oH

-65 m

-70 -75 -80

Wavelength, microns

F i g u r e 6 . 1 5 : Measured transmission characteristics of a fiber FP filter. The length of each grating was 0.3 mm, a 2.5 mm gap and with a peak-to-peak refractive index modulation of 5 x 10 -3. A theoretical fit to the data shows excellent agreement, although the peak transmission has not been fully resolved in the measurement [29]. A maximum extinction of >30 dB was measured.

W i d e - b a n d w i d t h (140-nm) fiber g r a t i n g F a b r y - P e r o t filters fabricated in b o r o n - g e r m a n i u m codoped fibers h a v e b e e n d e m o n s t r a t e d w i t h a finesse of b e t w e e n 3 and 7 [28]. Two identically chirped, 4-mm-long g r a t i n g s w i t h a b a n d w i d t h o f - 1 5 0 n m a n d reflectivity of > 5 0 % were w r i t t e n in t h e fiber, displaced from each o t h e r by 8 mm. T h e r e s u l t i n g F P i n t e r f e r e n c e h a d a b a n d w i d t h of 0.03 n m a n d a free-spectral r a n g e of 0.09 nm. A l a r g e r free-spectral r a n g e was obtained by overlapping the g r a t i n g s w i t h a l i n e a r d i s p l a c e m e n t of 0.5 mm. These g r a t i n g s h a d a b a n d w i d t h of 175 n m in t h e 1450-1650 n m w a v e l e n g t h window. A finesse of 1.6 w i t h a n F S R of 1.5 n m was d e m o n s t r a t e d . T h e s e fiber-grating FP-like devices m a y find applications in fiber l a s e r a n d W D M t r a n s m i s s i o n systems. A f u r t h e r possibility of opening up a gap w i t h i n the stop b a n d is to write two g r a t i n g s of slightly different B r a g g w a v e l e n g t h s at the s a m e location in the fiber [30] to form a moir~ fringe p a t t e r n . The physical r e a s o n w h y a b a n d pass r e s u l t s m a y be u n d e r s t o o d by noticing t h a t the p h a s e responses of the g r a t i n g s are not identical. Thus, at some wavelength, the p h a s e s can be out by ~r r a d i a n s . If the w a v e l e n g t h difference is m a d e larger, it is possible to create more t h a n one b a n d pass. The mechanics of producing such a b a n d pass h a v e been d e m o n s t r a t e d by

246

Chapter 6 Fiber Grating Band-pass Filters

slightly altering the angle of the incoming beams in between the writing of the two gratings [30]. Unless the angle can be measured accurately, it may be difficult to reproduce the results with precision. Two gratings can be superimposed in a fiber by writing one grating with a chirped phase mask [31] and then stretching the fiber before writing the second [32,33]. The basic principle of moir~ grating formation is discussed in Chapter 5. However, for clarity, we consider the interference due to two UV intensity patterns to produce a grating with the refractive index profile

An(z)= An[2 + 2 cos~27rZ~coS(~g ) ] \Ae]

(6.2.3)

in which the slowly varying envelope with period A e is a result of the difference between the two grating periods, and the chirped grating period is Ag. If the envelope has a single cosine cycle over the grating length (the grating periods have been chosen to be such; see Chapter 5), then the effect of the zero crossing of the envelope is equivalent to a phase step of rr/2 at the Bragg wavelength (see Chapter 5, Section 5.2.7). This grating is simple to simulate using the matrix method; the apodization profile of the grating can be specified to have n cycles of a cosine function, where n = 1 is a single cycle of a cosine envelope (see Fig. 5.18). The computed transmission spectrum of this type of a band-pass filter is shown in Fig. 6.16. The experimentally achieved result is almost identical to that shown in Fig. 6.16 [33], apart from the short-wavelength radiation loss apparent just outside the band-stop spectrum in the measured result. The problem with this type of phase-shifted grating has already been discussed: There remains a trade-off between bandwidth and extinction, although it is a convenient method of producing a multiple-band-pass filter by increasing the number of cycles of the modulation envelope.

6.3

The Michelson pass filter

interferometer

band-

The Michelson interferometer (MI) may be used as a fLxed-wavelength band-pass filter. Since the coupler shown in Fig. 6.17 splits the input power equally into the two ports, the light that is reflected from a single 100% reflection grating (HR1) is again equally split between ports 1 and 2. Thus, only 25% of the light is available in the pass band at port 2.

6.3

247

The Michelson interferometer band-pass filter

1.O 0.8-

0.6

-

"~ 0.4 r~ r~

0.2-

[..

0.0

1550.0

I 1551.0

1552.0

1553.0

1554.0

Wavelength, nm F i g u r e 6 . 1 6 : Transmission spectrum of a moir~ grating with a single period cosine envelope of the modulation refractive index profile over the length of the grating. This grating is formed by colocating two chirped gratings with slightly different center wavelengths.

F i g u r e 6 . 1 7 : A fiber coupler with a single grating in one arm. The output in port 2 is 25% of the input power in port 1. The transmitted signal at the Bragg wavelength at port 3 is (1 - R), where R is the grating reflectivity.

This a r r a n g e m e n t works as a n effective b a n d - p a s s filter despite t h e loss. However, t h e r e are m e t h o d s t h a t be u s e d to e l i m i n a t e the i n s e r t i o n loss of this filter. With two identical gratings, one in each a r m of the MI, 100% of the reflected light can be routed to port 2. The principle of operation was originally proposed by Hill et al. [34], for a g r a t i n g in a loop m i r r o r

248

Chapter 6 Fiber Grating Band-pass Filters

configuration. A similar device is shown in Fig. 6.18. The light reflected from HR2 arrives at the input port 7r out of phase with respect to light from HR1. Light from HR1 and HR2 arrives in phase at the output port 2, so that 100% of the light at the Bragg wavelength appears at this port. The through light is equally split at ports 3 and 4, incurring a 3-dB loss. However, the phase difference between the reflected wavelengths arriving at the coupler has to be correct for all the light to be routed to port 2. The first demonstration of such a device in optical fibers was reported by Morey [35]. This all-fiber band-pass filter was made out of a standard fiber coupler with fiber gratings written into the two arms. Stretching the gratings showed limited tunability, but no data was available on stability of the filter. Since differential changes in the ambient temperature between the arms can detune the filter, it is essential that the two arms remain in close proximity and t h a t the optical paths to and from the gratings be minimized. The fiber Michelson interferometer has been used extensively for sensing applications with broadband mirrors deposited on the ends of the fiber [36]. The principle of operation of the grating-based filter is a simple modification of the equations that describe the broadband mirror device. We begin with the transfer matrix of the fiber coupler [37],

- i sin(KL~)

cos(~J~c) J Bi '

where R and S are the output field amplitudes at ports 3 and 4, Ai and Bi are the field amplitudes at ports 1 and 2 of the coupler, L c is the coupling length of the coupler, and K is the coupling constant, which

F i g u r e 6 . 1 8 : The Michelson interferometer band-pass filter. All the input light is equally split at the coupler into the output ports. The identical gratings in each arm reflect light at the Bragg wavelength, while allowing the rest of the radiation through.

6.3

249

The Michelson interferometer band-pass filter

depends on the overlap of the electric fields E 1 and E2 of the coupled modes, K -

t o e 0 f~oo f+_oo (n2co(X,Y) 2 , 4P o oo oo - ncl)E 1 " E 2 d x d y ,

(6.3.1b)

where nco (x, y) is the transverse refractive index profile of the waveguides, ncl is the cladding index and, Po is the total power. For a small difference in the propagation constants, h/~ is small compared to the coupling coefficient, K. Under these conditions, very nearly all the power can be transferred across from one fiber to the other [38]. With Aft ~ 0 and (nco - ncz)/nco ~ 1, the following expression for the coupling coefficient can be use [39]: u 2 Ko[w(h/a)] K - 2 7rn c a 2 v 2 ~ll(W) "

(6.3.1c)

a is the core radius, and the normalized waveguide parameters u, v, and w are defined in Chapter 4, h is the distance between the core centers, and the modified Bessel functions of order 0 and 1, K o and K1, are due to the evanescent fields of the modes in the cladding. Assuming that there is only a single field at the input port 1 of the coupler, B i = O. Introducing gratings in ports 3 and 4 with amplitude reflectivities and phases, Pl exp[ir and/)2 exp[ir described by Eq. (4.3.11), the normalized field amplitudes at the input to the coupler in ports 3 and 4 are R3

A / / - trip 1

+ (6.3.2)

_ B4 _ [2i(2zrneffLf2 r $4 Ai - i o 2 P 2 sin(rJ~c)exp A +

]

,

in which the path lengths from the coupler to the gratings are Lfl and Lf2. The additional factors ~r1 and ~r2 include detrimental effects due to polarization and loss in arms 3 and 4. The output fields, R1 and $2, at ports 1 and 2 of the interferometer can be written down by applying Eq. (6.3.1a) again, with the input fields from Eq. (6.3.2). Therefore, S2

- i sin(KLc)

cos(KLc) J $4 "

In Eq. (6.3.3) the normalized field amplitudes R1 and $1 fully describe the transmission transfer function of the Michelson interferometer band-

Chapter 6 Fiber Grating Band-pass Filters

250

pass filter. Substituting Eq. (6.3.2) into Eq. (6.3.3), and remembering that Re(R, S) = 1/2(R, S + R*, S*), the transmitted power in each output port of the filter is the product of the complex field with their conjugate. By simple expansion and algebraic manipulation of the equations, the power transmittance at ports 1 and 2 can be shown to be 1

tl = ~ [ 2 ~ p 2 cos4(KLc) + 2 ~ p 2 sin4(KLc) -

sin2(2KLc)cOs ~] (6.3.4)

cho'2p~p2

1

(6.3.5)

t 2 = ~ [O~lfl 2 + O~2fl2 + 2trltr2PlP2 cos ~]sin2(2~abc),

where the phase difference 6 between the reflections from the two gratings is

~ = 2 [ 2 ~ e f f (Lf2 - Lfl ) +

r

r 2

"

(6.3.6)

Equations (6.3.4) and (6.3.5) describe how the transmitted power at the output depends on the path-length difference, the reflectivities, and the Bragg wavelengths of the two gratings in the arms of the Michelson interferometer filter. For a 50:50 coupler, ~a5c = r ignoring loss and polarization effects, Eqs. (6.3.5) simplify to

tl = -~

(p2 + p2)

111

t2 = -~

_

PiP2 cos 6

]

(p2 + p2) + PiP2 cos 3 .

(6.3.7)

(6.3.8)

Note that the power transfers is cyclic between the two ports, depending on themphase difference 6 and which is of paramount importance for the proper operation of the filter. This cyclic behavior is well known for unbalanced broad band interferometers, but in this device it is restricted to the bandwidth of the gratings. The choice of the gratings determines the wavelength at which the interference will occur. With the phase difference 6 = 2Nrr (where N -> 0 is an integer), all the power is routed to port 1. This phase can to be adjusted mechanically [40], thermally [41], or permanently by optical "trimming" of the path using UV radiation [53]. Detuning of the interferometer is an important issue for the acceptable performance of the band-pass filter. As such, there are two parameters, which are variables in a filter of this type. Assuming that the

6.3

251

The Michelson interferometer band-pass filter

bandwidths of the two gratings are identical (nominally identical lengths and refractive index modulation amplitudes), the p a t h difference m a y drift within the lifetime of the device, or the Bragg wavelengths m a y not be identical, or may change with time. Figure 6.19 shows how the band-pass at port 2 varies with changes in the p a t h length for two identical 99.8% reflectivity gratings. At zero phase difference, the transmission is a maximum. The rapid decrease in the band-pass peak with detuning of less t h a n half a wavelength shows t h a t phase stability is critical for the long-term operation of this device. As expected, the transmission drops to zero with a phase difference of 7r/2. In most practical cases, it is nearly impossible to m a t c h gratings in the two arms exactly, both in reflectivity (and therefore bandwidth) and the Bragg wavelength. The mismatches set a limit to the performance of a band-pass filter. Figure 6.20 shows the reflectivity spectra of two raised cosine apodized MI gratings, which are offset in their Bragg wavelength by 1% of the FW bandwidth. For the gratings shown, this t r a n s l a t e s to 0.01 n m difference in the Bragg wavelengths and m a y well be at the limit of the technology for routine inscription and annealing of the gratings.

1.00 0.75 o

-9 0.50

oil

E- 0.00 -0.0015

-0.0010

-0.0005 0.0000

0.0005

0.0010

0.0015

Normalised detuning, ( ~ - ~b)/~b

F i g u r e 6 . 1 9 : The band-pass characteristics of a Michelson interferometer filter showing how the band-pass peak varies with differential path-length difference between the two gratings as a function of normalized detuning. For the calculations, the grating parameters used are: refractive index modulation index amplitude of I • 103 and a length of 2 mm [42]. The numbers on the chart refer to the detunings as a fraction of the Bragg wavelength. The figure shows just how critically the path difference needs to be controlled for efficient operation.

252

Chapter 6 Fiber Grating Band-pass Filters

F i g u r e 6.20: Reflection spectra of two 4-mm-long raised cosine apodized gratings mismatched by 0.01 nm (A, B), each with a reflectivity of ~85%. C is the transmission of the band-pass filter with a path-length difference of 0.006 x ~b. D shows the light that appears in port I of the Michelson. To achieve better than -30 dB extinction (for D), the Bragg wavelengths must be matched to within 0.01 nm. E shows the rejected light in port 1 for cosine apodized gratings with the same Bragg wavelength mismatch. The in-band rejection is never better than - 28 dB. With stronger gratings, the Bragg wavelengths have to be even better matched.

The pass band of the filter generally does not suffer from such a small wavelength detuning. Since the reflectivity ensures t h a t only the reflected signal appears in the pass-band with typical insertion losses of between 1 and 0.3 dB [43], it is the r e m n a n t signal t h a t appears in the through port (in the Michelson, it is port 1) t h a t is difficult to suppress. The detuned Bragg wavelength of the gratings translates into an additional imbalance in the path difference of approximately 1 mradian. While UV trimming can balance the paths very accurately, the small difference in the Bragg wavelengths of the two gratings remains. Despite this error, a rejection of greater t h a n 30 dB has been reported [43] and is certainly not an easy achievement, requiring the matching of the Bragg wavelengths to - 0 . 0 1 nm. The theoretical spectra shown in Fig. 6.20 are in excellent qualitative agreement with the results of low-insertion-loss band-pass filters fabricated in optical fiber with matched gratings in the close proximity of a coupler [43]. Chirped gratings can be used in the Michelson to broaden the pass bandwidth [44]. With further mismatch in the Bragg wavelengths, the rejection in port 1 deteriorates. One can no longer have a high isolation, since there

6.3

253

The Michelson interferometer band-pass filter

is less overlap between the bandwidths of the gratings. The conditions approach the case of a single grating in the coupler arm, when there is no overlap of the grating spectrum. Thus, at least 25% of the input power appears at both ports I and 2. While the rejection becomes poor, the bandpass suffers because the bandwidth decreases as a direct result of the limited overlap. Figure 6.21 shows the reflection spectra of gratings in a Michelson t h a t have been detuned by one-quarter of the unapodized FWFZ bandwidth (to the first zeroes). The refractive index modulation amplitude is 1 x 10 -3 and the gratings are 4 mm long. Since the interferometer has been detuned as a result of the difference in the Bragg wavelengths, at zero phase difference the band-pass output is not at its m a x i m u m (small crosses). As the path difference is changed to ~r/2 radians (triangles), a dip begins to appear in the band pass, and with ~r phase difference (squares), "bat-ears" begin to appear, since at the edges of the band pass,

/L.

1.0 0.9 0.8

,

0.7 0.6 r

0.5 0.4

~

t'

/,, ~ R X

G1

,--------

>h

~

RX BP3 D Output (pi phase dill) ~ .__ l x Output (0 phase diff) I i~ ~: ~9 Output(pi/2 phase ~ff)~ 1~ i 9

'12Z

l

>'s |

~t

~C

o~

D.~X

0.2

,

[ / r/ ! ii/ ~ u•

A

Itl/1

j

0.0

-6.0E-4

" "" -4.11E-4

-2.0E-4

0.0E+0

N o r m a l i z e d detuning, ( X -

2J IE-4

4.0E-4

6.0E-4

~bragg)/~bragg

F i g u r e 6 . 2 1 : The band-pass characteristics show that with slight detuning (0.25 x FW bandwidth) between the two Bragg gratings, a slight reduction in the peak transmissivity occurs (crosses). However, there is an added benefit: reduction in the energy transmitted in the wings of the gratings, i.e., apodization occurs. Note that with larger path length difference, "bat-ears" appear on either side. These normally appear in the rejected port I (squares).

254

Chapter 6 Fiber Grating Band-pass Filters

there is little overlap of the reflected spectra. Note t h a t at some Bragg wavelength detuning, the interference of the reflected light at the coupler forms moir~ fringes, and apodization of the band-pass spectrum begins to occur. In Fig. 6.21 (crosses), note the reduction of the side lobes as the dissimilar phases in the overlapped spectrum tend to cancel the formation of the side lobes. The filter rejection becomes worse w h e n the detuning is one-half of the FW bandwidth, as shown in Fig. 6.22. In this case, the zero path difference is well off the optimum for band-pass operation (triangles), while squares show the band pass response at ~rphase difference between the gratings. Although this spectrum is still not the optimized output, note the strong apodization in the wings. The nonoverlapped high-reflectivity (~ 100%) region (within the bandwidth of each grating) averages to approximately 25% of the input power, as in the case of the single-grating Michelson device.

1.0

I

"

!

~

RX GI RX G4

0.9 0.8

G 4 + G I (pi

x

G4 + GI (pi/2 G 4 + G I (0

1

phase diff) phase d i f f phase diff)

a

0.7

F

/i

0.6

9I

ol :' Dj io

r

m 0.5

!

D 0 D

0.4

0.3 0.2

0.1

A x--

0.0 -6.0E-4

-4.1}E-4

-2.0E-4

0.0E+0

N o r m a l i z e d detuning, ( ~ -

2.0E-4

4.0E-4

6.0E-4

~bragg)/~bragg

F i g u r e 6 . 2 2 : Two gratings detuned by approximately 0.5 x bandwidth of the grating. The band-pass characteristics are sensitive to the path-length difference between the Bragg reflection peaks due to differential phase response of the gratings. With detuning, the optimum band-pass shifts from the normal zero phase difference for matched Bragg wavelength case and develops additional structure, although apodization occurs, reducing the reflection in the wings.

6.3

The Michelson interferometer band-pass filter

6.3.1

The asymmetric filter

Michelson

255

multiple-band-pass

Figure 6.19 showed how output power in port i varies with p a t h difference ~/. The reflected power within the entire grating spectrum is exchanged between port 1 and 2 so long as the detuning ~/~

A2 2Ahg'

(6.3.9)

where hag is the FWFZ b a n d w i d t h of the grating. With larger p a t h differences, neff~Lf = ne~Lta - Lf2), the phase variation 8 as a function of wavelength, according to Eq. (6.3.4), becomes substantial across the bandwidth of the grating. Thus, the single uniform band pass of the filter begins to split into a sinusoidal wavelength with wavelength, restricted to the b a n d w i d t h of the grating [42]. Figure 6.23 shows the reflection spectrum of an apodized grating MI and the band-pass output of the filter with a p a t h difference of 0.667 mm. Within the reflection spectrum of the grating, the band pass has three peaks. Each peak automatically has the m a x i m u m transmission possible for the band pass, i.e, determined by the reflectivities from the gratings. With the detuning shown in Fig. 6.24, nine peaks a p p e a r within the same b a n d w i d t h of approximately +_0.0005 detuning. Being a nonreson a n t device, the output is simply equivalent to the interference between

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

0 ~ -10 .,~

,

~i

-20 -30 -40 -50 -60 Normalized detuning ,( )~agg-)~)/~agg

Figure 6.23: The reflectivity and band-pass spectrum of the asymmetric Michelson interferometer. The one-way path imbalance is 0.667 mm and the apodized gratings are 4 mm long with a Anmod of I X 10 -3 [42].

256

Chapter 6 Fiber Grating Band-pass Filters

-0.0015 0

-0.001

-0.0005

0

0.0005

0.001

0.0015

-lO .~ -2O -30

~ -40 -50

-60 Normalized denning, ( ~bmgg]~)/~bragg

F i g u r e 6 . 2 4 : The apodized reflection (dashed line) and band pass (continuous line) of the asymmetric Michelson interferometer, with a path difference of 2.67 mm. The output is sinusoidal as in the case of a low-finesse FP interferometer.

two beam as a function of phase difference, hence the sinusoidal variation, also the case with the low-finesse FP interferometer. The wavelength difference 6~ between the peaks of the band pass is ~2

SA =

2neffAL f + Ar

(6.3.10)

where Ar is the differential phase of the two gratings, which becomes i m p o r t a n t when the gratings are dissimilar, for example, chirped. Using Eq. (6.3.10) one can calculate the exact n u m b e r of pass bands within the bandwidth of the gratings. Note t h a t with Bragg-wavelength detuned gratings, the r e s u l t a n t bandwidth for the pass bands is the difference between the individual bandwidths of the gratings. The measured response of such a filter is shown in Fig. 6.25. The extinction is 28 dB. There are three possible combinations for a r r a n g i n g chirped gratings in the Michelson interferometer: both gratings with the same sign of the chirp, either both positive or both negative, or with opposite chirp. In Fig. 6.26, the first two a r r a n g e m e n t s are shown (A and B). The difference between A and B is t h a t the dispersion of the gratings has been reversed, and t h a t a pair of such filters may be used to compensate for most of the dispersion in each filter. The transmission band pass of the identical-sign, linearly chirped grating Michelson interferometer with ~ L f -- 1.724 m m is shown in Fig. 6.27. The gratings are 5 m m long with a chirped b a n d w i d t h of 10 nm.

6.3

257

The Michelson interferometer band-pass filter 1542

1540

1544

1546

1548

1550

1.0"

BP 0.8

-

Gratiag 1

\

~' ~ 0_5=~'~ .~'~

~ @ Z

!l i

03-

0.0

il i

A

_ _ ~ Wavelength, nm

Figure 6 . 2 5 : The reflection spectrum of each grating (1 and 2) measured in situ by bending the fiber in the other port to induce loss: hence the -25% reflection.

The normalized band-pass filter spectrum (BP) as a result of a path difference ALwof-1.33 mm [42].

C h i r p e d gratings Port 3" Port 1" I N P U T

Port 2:

OUTPUT

i,

~Bragg

50:50

L[LiLtillliliillill I I IIIIIIIIIIIIIIII

A

I I I

I

50% Tx

I

Port 4" 50% Tx

I I I lllllllLI lib III B

L I I lllllllllillll I Figure 6 . 2 6 : Chirped gratings in configurations A and B, each with a path imbalance of ALwbut with reversed sign of the chirp.

The unapodized gratings have a Anmo d of I x 10 -3. The pass bandwidths of the channels are all identical and equal to the width of the channel spacing. The repeated pass bands can be adjusted by altering the path imbalance; in a demonstration, the paths were adjusted by stretching one arm of the interferometer to fit a grid of 1.1 or 2.2 nm using two 15-nmbandwidth chirped gratings [45].

Chapter 6 Fiber Grating Band-pass Filters

258

1 i~

o.8

--

"\

o~ ,~

0.6-0.4

--

0.2

--

/

0

1545

Output

!

!

!

1550

1555 Wavelength, nm

1560

1565

F i g u r e 6 . 2 7 : Band-pass and reflection spectra with two identically chirped gratings (Lg = 5 ram, chirp = 10 nm, and LkLf = 1.724 ram).

When the sign of the chirp of one of the gratings is reversed, the band-pass transmission characteristics change from regular repeated pass bands to a variable pass band. The p a t h difference between the two gratings is reduced to zero at some wavelength. A gap opens at this point and the transmission is no longer uniform as in the previous cases. Ignoring dispersion, the phase difference between the light reflected from these two weakly reflecting, chirped gratings with a chirp of hag nm relative to the wavelength ~o in the center of the grating, is

+

=.

where Lg is the length of the grating. It is a p p a r e n t from Eq. (6.3.11) that the detuning 8 = 0 when a = ao - •

9

(6.3.12)

IfM.,/= 0, 8 = 0 at the wavelength ,t = io. For a fixed chirp bandwidth, the detuning can be reduced to zero at any wavelength within the bandwidth of the grating by tuning M_,[. In Eq. (6.3.11) we have assumed that the lengths of the two gratings are identical. This need not be the case; it is enough t h a t the bandwidth are identical, so t h a t we have the extra p a r a m e t e r t h a t can be adjusted. This also applies to the previous eases in which the sign of the chirp for both gratings was identical. The pass-

6.3

The Michelson interferometer band-pass filter

259

band period is now chirped, since the variation in the detuning is no longer constant close to the phase-matching wavelength. Figures 6.28 and 6.29 demonstrate the effect of the counter-chirp of the gratings for the more general case of dissimilar length gratings. At the top of Fig. 6.28 is shown a schematic of the third combination for the chirped gratings (C) and the relative positions, orientations and lengths

F i g u r e 6 . 2 8 : Above the chart is shown the arrangement of the gratings (C) used in this simulation of the asymmetrically placed grating Michelson interferometer BP with identical chirp bandwidth but dissimilar lengths (5 and 10 ram). Notice the chirp in the period of the pass bands. The reflectivity of one of the gratings is also shown.

Figure

6 . 2 9 : The band-pass response with a 3.448-mm path difference.

260

Chapter 6 Fiber Grating Band-pass Filters

of the gratings. The first case is for 10- and 5-mm-long gratings, each with a chirped bandwidth of 10 nm and with a detuning of 0.344 mm (Fig. 6.28). The gap opens up close to one long-wavelength end of the grating, while with a larger ALw of 3.44 m m in the second case, the gap shifts to the short wavelength end (Fig. 6.29). In either case, moving away from the phase-matching point [Eq. (6.3.12], the oscillations in the transmission spectrum become more rapid. There are important issues relating to the asymmetric grating Michelson interferometer band-pass filter. First of all, any interferometer is sensitive to differential temperature and strain. The asymmetric interferometer is especially so; however, with fiber leads to the gratings kept in close proximity, the only region, which needs stabilization, is the differential path. For sensing applications, the broad bandwidth of the chirped grating is a distinct advantage. Stabilization of the paths may be done in a number of ways, for example by the application of a special polymer coating [46,47], or use of a substrate to compensate for the thermal expansion [48]. The filter has very high extinction, but the stability is polarization sensitive, and the transfer characteristics are sinusoidal with wavelength. The period and chirp are easily designed into the filter. Applications may be found in signal processing, sensors, multiplexing, and spectral slicing within a well-defined bandwidth. Ideally, it would be suited to fabrication in fused fibers, close to the coupler, or in planar form.

6.4

The Mach-Zehnder band-pass filter

interferometer

The dual-grating Mach-Zehnder interferometer band-pass filter (GMZIBPF) overcomes the severe limitation of the Michelson interferometer filter -- the loss of 50% of the through transmitted light -- by recombining the output at a coupler, as shown in Fig. 6.30. The scheme was proposed by Johnson et al. [49], and using etched gratings in a semiconductor waveguide Mach-Zehnder interferometer, Ragdale et al. [50] were able to show a device operation. A major drawback of a device fabricated in this way is the high intrinsic losses due to scatter, absorption, and input/ output coupling, although large bandwidths are possible due to the use of short gratings resulting from the large modulation index of the grating (air and semiconductor). Additionally, once the device has been fabricated,

6.4

The Mach-Zehnder interferometer band-pass filter

261

F i g u r e 6.30: The Mach-Zehnder interferometer used as a band-pass filter. UV trimming of the paths has been shown to be a powerful tool for rebalancing the paths such that 100% of the light reflected from the gratings appears at the output port on the left [53,43]. By adjusting the phase difference at the coupler beyond the gratings, the output may be directed to either output port of the coupler.

phase a d j u s t m e n t between the guides to balance the interferometer is difficult without active control. The first demonstration of a working band-pass device using the principle of the M a c h - Z e h n d e r interferometer (MZI) with two identical UV written gratings was in planar-Ge:silica waveguide form [53]. The device was an MZI with overclad ridge waveguides, which h a d been photosensitized using hot-hydrogen t r e a t m e n t [51]. "UV trimming" was used to balance the interferometer after the gratings were written, d e m o n s t r a t i n g this powerful technique also for the first time [53]. This is shown Fig. 6.30. "UV trimming" relies on photoinduced change in the refractive index to adjust the optical path-length difference. The 6-dB insertion loss for a single-grating band-pass filter was overcome and reducer to - 1 . 3 4 dB for the fiber pigtailed device, by UV trimming; much of it comprised coupling and intrinsic waveguide loss. The fiber gratings had a reflectivity of - 1 5 dB each and were well matched in wavelength. Approximately 10% of the light was reflected into the input port. Although the insertion loss of this MZI-BPF was not as low as l a t e r devices, the p l a n a r MZI has the advantage of being extremely stable to environmental effects. Since the demonstration, several groups used this scheme of UV t r i m m i n g in fiberbased MZIs to demonstrate band-pass filters with better extinction and

262

Chapter 6 Fiber Grating Band-pass Filters

insertion loss [43,52]. For proper operation, the output coupler needs to be balanced, requiring trimming on the RHSs of the gratings. Indeed, it is simple to observe that the device can be used as an add multiplexer at the dropped wavelength if the same wavelength is locally injected at the port marked "Insert" (RHS, bottom). This wavelength will be routed through to the Add port performing the basic Add-Drop multiplexer function. Many of these MZIs may be cascaded to perform a multiple-wavelength band-pass function. Cullen et al. [52] demonstrated a compact GMZI-BPF in fiber form. The device, based on two 50:50 splitting fused fiber couplers fabricated in boron-germania codoped fibers (Core-cladding index difference An = 7 x 1 0 - 3 and core diameter of 7 ttm), with 1-meter tails. The two pieces of fiber were first tapered and fused to a constant diameter of 100 ttm over a length of 20 mm. A 3-dB coupler was formed by further tapering one end of the fused region, until the desired splitting ratio of 50% was achieved. When the second coupler is made, if the path lengths in the two arms are identical, 100% of the light will appear in the crossed state, i.e., in port 4 when port 1 is excited. Allowing for fabrication loss and slight imbalance, between 95 and 99% of the light was available at port 4 after the second coupler was fabricated under the same conditions. The finished device had ~5 mm of space in the parallel fiber section between the couplers for the inscription of the gratings and for UV trimming. The advantage of such a structure is the relative stability of the MZI, since the couplers and the fused fiber regions are so close together. Any ambient temperature fluctuations affect both fibers equally. This was established by a measured change in the output power of the MZI of

/'/

~short

ii

[fiber core

,/=......... -',x-~......................-~

"%//'Reflection'", ............. (a)

(b)

........................ Transmission

Figure

6 . 4 5 : Light radiated from the STG and (b) from the LPG.

290

Chapter 6

Fiber Grating Band-pass Filters

length dependence of the loss. There are two bounds to the loss spectrum, one on the short- and the other on the long-wavelength side: Light radiated out of the fiber core subtends a wavelength-dependent angle ~A) to the counterpropagation direction (STG) and copropagating (LPG), which depends on the inclination of the grating and period. For the STG, this angle of the radiated light at wavelength A in the infinite cladding is easily shown to be l

nclad

where t~gis the tilt of the grating with respect to the propagation direction, and N is the order of the grating. The angle at which the light exits from the side of the fiber varies as a function of wavelength and therefore can be used as a band-pass filter. The bandwidth of the radiated light can be shown to be approximately AA ~ Agsin2(8~)

(6.8.2)

2 cos(Sg) "

However, the phase-matching condition alone does not determine the peak wavelength, in the general case when the grating is titled; the overlap integral together with the phase matching alters the spectrum and shifts the wavelength of maximum loss (see Chapter 4). Typical transmission loss and reflection spectra for a strong STG are shown in Fig. 6.46a, and

1480 1500 0 ~ ~ . . -5 m -10 "o -15

1520 I

1540 l

3 -2o 8

i_~-2s

1450

~i !I

,~i

-5-

-30 ~"

~

-2o

-35

~-

-25 -

-40

~ ~ ~ r

~'~,~~" i ~

Wavelength, nm

(a)

1475

o - ~ ~

-25

E -35 -30 -40

-5o ~,~,!~

1560 1580 ,"-'-,;--" = ' 0 -5 -10 -15 -20 ~"

-45

-30-

-50

-35 .i

1500

,.,

1525

1550

1575

1600

1/

Wavelength,nm

(b)

F i g u r e 6.46: The transmission loss (and reflection) of (a) a 4-mm-long sidetap grating filter and (b) LPG filter with a 400-micron period, both written in a boron-germania codoped fiber.

6.8 Side-tapand long-periodgrating band-passfilters

291

the transmission loss spectrum of an LPG, in Fig. 6.46b. Both gratings were written in the same fiber. The STG has been used as a spectrum analyzer by Wagener et al. [88]. A chirped grating blazed at 9 ~ to the propagation direction was used to out-couple light from a fiber. The chirped grating had a decreasing period away from the launch end of the fiber. Since the angle 0(A) subtended by the radiated light at a wavelength ~ becomes smaller with reducing pitch [Eq. (6.8.1)], the focus of the light coupled out at different points is a function of the wavelength. The focal length is inversely proportional to the wavelength of the radiated light as [88] f(~)=

A~

L~ sin[0(~)]

co s( 0 g )

(6.8.3) '

where Ag is the nominal period of the chirped grating, n is the refractive index of silica, and Lg and t~g are the length and the change in the period of the grating due to chirp (in nm), respectively. The radiated light was detected by a 256-element photodiode array, the center of which was arranged to be at the focus of the light at ~c, the wavelength radiated by the center of the grating. A schematic of the device is shown in Fig. 6.47.

~

256 element detector array

ing prism

~short

IIII, Chirped STG

~short Core

Square-cladding cross-sectionfiber F i g u r e 6.47: A schematic of the in-fiber chirped STG spectrum analyzer (after Ref. [88]).

292

Chapter 6 Fiber Grating Band-pass Filters

A weak, 20-mm-long grating (Ag = 547 nm) with a chirp in the period of 1.92 nm (___0.96 nm) was used to tap ~5% of the light over a 35-nm bandwidth. An index-matched prism was placed in contact with a fiber of square cladding cross-section to promote good adhesion, to direct the light to the photodiode array. The effective focal length was 160 mm. The resolution of the spectrometer was demonstrated to be 0.12 nm with a measured bandwidth of 14 nm, an insertion loss of '

15

-20

(D

~ 10 Gb/sec is possible for optical fiber transmission [32]. This design relies on the high-differential gain and low intrinsic chirp of a strained MQW, AR-coated front facet FP laser and the high-speed chip design using semi-insulating blocking layers. The linewidth of this laser was measured to be 40 kHz ( - 13 GHz roundtrip resonance; 8-mm external cavity), with - 3 dB modulation bandwidth o f - 1 5 GHz. The frequency response of the laser for different bias currents is shown in Fig. 8.11. The external cavity resonance is clearly visible as the current is increased to 100 mA. Measurements have shown t h a t the chirp of this laser remains

2~'1

+-5-"

(8.4.7)

374

Chapter 8

Fiber Grating Lasers and Amplifiers

Equation (8.4.7) states that the loss of the second mode must be greater than a third of the single pass gain plus the cavity roundtrip loss for the first mode. The reflectivity of the grating may be computed by the methods presented in Chapter 4 and used to determine the reflectivity for a given length of doped fiber with an unsaturated gain of ao per meter. With the gratings written in highly doped erbium-doped fiber, the additional gain within the gratings must also be taken into account, since the effective reflectivity is increased [62]. The best region for single-mode operation is when the free-spectral range is twice the expected shift in the lasing frequency induced by perturbations and cavity length changes. This is greatly assisted by making the cavity as short as possible.

8.4.1

Single-frequency

erbium-doped fiber lasers

Erbium-doped-fiber grating lasers (EDFGLs) offer a simple and elegant solution for wavelength selection, providing a very narrow linewidth as well as a high degree of wavelength stability. They are also compatible with optical fiber systems and can be easily integrated with other fiber components, such as WDM couplers and fiber isolators. Tests performed on an externally modulated single-frequency EDFGL have confirmed its robust suitability for error-free high-speed application in transmission systems [50]. The laser is fabricated with 600 ppm GeO2:AI203doped silica fiber with a refractive index difference of 0.023 (core diameter of 2.6 ttm) and cutoff at 880 nm. The tight confinement ensures high efficiency, and aluminum reduces the concentration-quenching effects that reduce the lifetime of the upper laser level, also leading to instabilities [63]. The gain of this fiber was reported to be - 1 0 dB/m, with an overall length of the laser of 4.4 cm, including gratings (98% O/P coupler and ~100% broadband high reflector), using the linear cavity design shown in Fig. 8.15. Pumped at 1480 nm, the laser is operated close to threshold to ensure singlemode operation and amplified in a MOPA configuration through an optical isolator. The packaged laser is sensitive to vibration that drives relaxation oscillation at a frequency o f - 1 5 0 kHz. These oscillations can be actively controlled by using a feedback scheme to control the diode-pump laser and reduced to insignificant levels [50,64,65]. The error-free performance of several EDFGLs in transmission experiments at 2.5 and 5 Gb/sec been have reported [66,50,67], using external

375

8.4 Erbium-doped fiber lasers

Mach-Zehnder modulators. Upto 60 mW of single-frequency power has been achieved using a MOPA configuration [68]. Other configurations for single-frequency operation use long gratings with a bandwidth less than the cavity mode-spacing [69,70], and operation at 1 micron using Nd:doped fiber has been shown with intracore gratings [71].

C o m p o s i t e cavity l a s e r s There are several methods for achieving single- and multifrequency operation of EDFGLs. As outlined already, short lasers with narrowband reflectors are simple candidates; however, a composite cavity topology can enforce stable single-frequency operation by longitudinal mode control, adapted from semiconductor lasers [72-75]. The principle relies on a small additional feedback element in the form of a short Fabry-Perot, which modulates the gain spectrum of the main fiber laser cavity. Figure 8.16 shows the linear cavity configuration. The basic laser cavity gratings have reflectivities of 0.9 and 0.8 with a weaker reflection of 0.1 as the external reflector. The gain of the composite cavity is modulated, increasing the discrimination between the modes. Since the lasing mode is influenced by the composite cavity, a single mode tunes with temperature changes but does not exhibit mode hops [53]. The 10-mm-long high erbium dopant concentration fiber (120 dB/m absorption at 1530 nm) is spliced to fiber gratings, forming a composite cavity - 7 cm long; 980-nm pumping with a Ti:sapphire laser showed a threshold of 50 mW. The linewidth of this laser is - 4 0 kHz using conventional heterodyne techniques. The gain

FS G1

b

~

FS / G2

G3

IIIll[[ Er doped fibre[ Illt1111 blI]ll[I

N

outp

F i g u r e 8.16: A schematic of the composite cavity single-frequency EDFGL [53].

376

Chapter 8 Fiber Grating Lasers and Amplifiers

bandwidth of such a laser with and without the extra etalon is shown in Fig. 8.17. With the external etalon, the gain is modulated at a frequency separation determined by the spatial separation and reflectivities of the gratings. The simulation in Fig. 8.17 shows the composite reflection spect r u m of the two gratings without the additional feedback (dashed curve) and with feedback (solid curve). In this laser, the period of the frequency separation is 28 GHz without feedback and --7 GHz with the etalon approximately half the mode spacing of the composite laser. The use of a very short gain region with respect to the cavity length (a factor of 3-4) eliminates the relaxation oscillation observed in other cavity designs [50] using erbium fiber. Composite fiber gratings with ring or loop mirror cavities [76] are other possible configurations, and for single frequency operation with intra-cavity frequency selector [77]. An example of this cavity is shown in Fig. 8.18 in a loop mirror arrangement. In this cavity, the loop mirror is a broadband mirror, while the external fiber Bragg grating is a bandselecting element. The isolators inside the loop-mirror ensure unidirectional operation, while the incorporation of an ultranarrow band-pass

x~oG N

.~ 04 ?

FSR-15GI-lz

02 O0 .... -20 -! 0 0 I0 20 Frequency shift, Gitz

F i g u r e 8.17: The reflectivity and mode selection spectra of the coupled-cavity EDFGL. Laser with feedback (solid line), and laser without feedback (dashed line) (from: Chernikov S. V., Taylor J. R., and Kashyap R., "Coupled-cavity erbium fiber lasers incorporating fiber grating reflectors", Opt Lett 18(23), 2023 (1993). (after Ref. [53])).

8.5

377

The distributed feedback fiber laser

Figure 8 . 1 8 : The loop mirror cavity for single-mode operation, incorporating a DFB band-pass filter and an erbium-doped fiber amplifier (after Ref. [77]).

DFB fiber Bragg grating (see Chapter 6), also inside the loop, enforces single-frequency operation. The laser may be tuned by applying compressive or extensive strain on the intracavity DFB grating or, in the absence of the DFB grating, the external grating. Single-frequency operation of such a laser with a 0.075-nm band-pass DFB grating shows a linewidth o f - 2 kHz, with side-mode suppression of 50 dB. However, the long cavity with a mode spacing of 11.4 MHz mode hops and requires the use of stabilizing elements [77]. Replacing the DFB band-pass intra-cavity filter by an acousto-optic tunable filter (AOTF) may extend the principle of this type of a laser. Ramping the AOTF sweeps the output frequency of the laser with 10 1530

1540

1550

1560

1570

Wavelength, nm

F i g u r e 8 . 2 7 : The ASE spectrum of a saturated erbium amplifier without and with a composite STG gain equalizing filter [122].

8.8

389

Gain-flattening and clamping in fiber amplifiers

With this information, the filter is fabricated with the amplifier at its operating inversion level, allowing live gain tailoring. In this instance up to nine individual STGs were written to m a t c h the variation in the gain. Each grating can be ~1 m m long, m a k i n g the entire gain equalization filter to be less t h a n 10 mm. Such a filter m a y be written using a single phase m a s k appropriately designed to give the desired loss at each wavelength, by scaling the length of each grating or with an appropriate amplitude shading [123]. A distinct advantage of the STG is t h a t the uncompensated t e m p e r a t u r e sensitivity of the loss spectrum is similar to t h a t for Bragg grating, m a k i n g the filter intrinsically stable. With t e m p e r a t u r e compensation as with Bragg gratings, the variation in the loss spectrum m a y be eliminated altogether over the required operating t e m p e r a t u r e range. The tilt angle for the STG is chosen to minimize back-reflection into the guided mode (see Chapter 4). The transmission and reflection spectra of two STGs with peak-loss wavelengths s e p a r a t e d by ~ 10 n m are shown in Fig. 8.28. The combined transmission loss of the two gratings it ~12 dB. The first grating is written at a blaze angle close to t h a t required for a m i n i m u m reflection, while the second is written at a larger angle to increase the b a n d w i d t h of the composite filter. Each grating has a loss of approximately 6 dB. The first STG, which peaks at the shorter wavelength, has a reflectivity o f - 3 5 dB, while the unoptimized longer wavelength loss STG shows an increased reflection of ~21 dB. Typically, the gain variation in the amplifier spectrum requires each STG to have a

1540

1520

1560

1580

O-

~

o~ ~ - l O "i9

9

= ~

-30

~ & r~

,

Transmission Loss

///~"-,,

Reflection

-40

9 -50

.... ,...,_,~.:_,.~ ,,.,,.,,~.,,~.~,,,~,~.,,,.,,.

,.

-60 Wavelength, nm

F i g u r e 8 . 2 8 : The transmission and reflection spectra of two STGs written in the same fiber. The 6-dB peak-loss STG 1 at the shorter wavelength has a reflection of -35 dB. The second unoptimized STG at a larger tilt angle has a higher reflection of - 21 dB.

390

Chapter 8 Fiber Grating Lasers and Amplifiers

peak loss of less than 3 dB, resulting in a maximum back-reflection of < - 4 0 dB. Thus, a concatenation of STGs may be used effectively to flatten the gain of an optical amplifier, with low back-reflection. The design of the fiber to alter the bandwidth of the filters has been discussed in Chapter 4. This approach allows finer structures in the gain spectra to be matched more closely [124]. The application of LPGs for tailoring the gain of optical amplifiers has also attracted interest. The main feature of the LPG is the coupling of the guided mode to a forward-propagating cladding mode, one of which is selected from a large number, to induce the desired loss at the appropriate wavelength within the gain spectrum. It should be remembered that several mode interactions, widely separated in wavelength, occur in tandem for a given grating period. As such, LPGs have been used to equalize the gain of erbium amplifiers [125,126] and as ASE-suppressing filters. The technique used for forming the gain-equalizing filter is identical to that for the STG and has been already described [122]. There are major differences between the STG and the LPG. The latter exhibits more than a single loss peak separated by ~30-60 nm, depending on the type of fiber used for the filter. Written in standard telecommunications fiber, the temperature sensitivity of the LPG is roughly 4-5 times that of the STG. However, it has a low back-reflection into the guided mode of ~ - 8 0 dB. Unless the LPG is fabricated in special temperature-stabilized fiber, the amplifier gain equalization remains temperature sensitive, leading to gain tilt. Finally, the wavelength of the peak loss is a function of the refractive index of the material surrounding the cladding. With an appropriate low-index polymer coating, the cladding mode resonance is made insensitive to the ourrounding material. The LPG has been used extensively in gain equalization of amplifiers and remains an important component. Another method of equalizing the gain of an erbium amplifier is by the use of two or more apodized reflection gratings in series with an optical isolator. The resultant spectrum is shown in Fig. 8.29. Gain equalization to approximately ___0.5 dB may be achieved with this simple arrangement. Since gain flatness of the optical amplifier with filters is dependent on the level of inversion, it becomes particularly attractive to combine the filter with all-optical gain control, which is considered in the next section.

8.8

391

Gain-flattening and clamping in fiber amplifiers 1520

~

0

o

-9 t~

-2

-~9

-4

t-

"6

E F-

1530

-8

1540

1550

1560

1570

/ //

/

Gratings( 1534/1559)1 Tx + A S E I

-10 W a v e l e n g t h , nm

Figure 8.29: The simulated gain spectrum of an erbium amplifier equalized by two reflection gratings of lengths 0.2 and 0.061 mm centered at 1534 and 1559 nm. (The refractive index modulations for the two gratings are 3.5 x 10 -3 and 1.06 x 10-3).

8.8.2

O p t i c a l g a i n c o n t r o l by g a i n c l a m p i n g

There are a variety of ways of stabilizing the gain of erbium-doped fiber amplifiers. In particular, sampling the state of the amplifier and deriving some sort of feedback, for example, signal levels [127], ASE [128], or a dedicated probe [129], to adjust the amplifier's pump power, or sacrificial injected signals have also been proposed [130,131]. These in t u r n limit in the frequency response by introducing electrical delays in the feedback loop. A simpler and more elegant all-optical approach to gain stabilization of an erbium doped fiber amplifier was first reported by Zirngibl [132], using lasing action in a ring cavity configuration. In a homogeneously broadened system, the inversion and therefore the gain remains constant irrespective of input signal level or the number of input channels. The amplifier remains robust against transients and to the switching of channels, so long as the amplifier continues to lase at some wavelength within the amplification window. The gain is maintained at the expense of the flux in the lasing mode. This "gain-clamped" amplifier is especially useful for cascading and in dynamically changing optical networks. The amplifier design is greatly simplified by the use of a linear cavity made with narrowband, highly reflecting Bragg gratings [133]. Delevaque et al. demonstrated a gain-clamped erbium amplifier lasing at 1480 nm with the aid of narrowband grating reflectors, pumped at 980 nm.

392

Chapter 8

Fiber Grating Lasers and Amplifiers

The properties of all-optical gain-controlled amplifiers, pumped at 1480 nm, and lasing at longer wavelengths, have been studied by Massicott et al. [134]. The cavity configuration used for gain control, pumped at 1480 nm, is shown in Figure 8.30. The amplifier cavity contains a length of erbium-doped fiber with two narrowband Bragg-matched fiber grating reflectors. Along with these gratings, a STG filter with a specified intracavity, loss is included close to the output end to control the intracavity loss and reduce the effect of stray reflections. Above a certain threshold pump power at which the cavity gain equals the intracavity loss, lasing occurs at a wavelength ~1, clamping the gain across the gain bandwidth due to the homogeneous nature of the transition. With an increase in the pump power, energy is stored in the lasing flux, while maintaining the inversion, and therefore the gain. Signal wavelengths experience a fixed gain up to a certain critical input level, at the expense of the lasing flux. Once the input signal is large enough to extract all the energy from the lasing mode, the amplifier ceases to lase. Thereafter, the amplifier inversion (and gain) is uncontrolled and is dependent on the pump power and signal levels as for a normal erbium-doped fiber amplifier. Figure 8.31 demonstrates the automatic optical gain controlled amplifier in operation. The amplifier consists of a 25-m length of erbium-doped fiber with a core diameter of 5.3 ttm and refractive index difference of 0.013. The peak saturable absorption of the fiber is 6.1 dB/m with a background loss of 8 dB/km measured at a wavelength of 1.1 ttm. The laser cavity is defined by two Bragg grating reflectors at 1520 nm, written in hydrogen-loaded GeO2-SiO2 fiber. The reflectivity of each grating is 94% with a 3-dB bandwidth of less t h a n 0.4 nm. The splices dominate

Signal input ;L,

~.

,/Er3+ ',,, !doped ~i Intracavity ..,, fiber / / loss x~ WDM Fo----IIII~... .............. i~..........:::::............. --:::::::'" II1', ~ reflector j reflector ~., T

*------

Laser cavity

Pump ;Lp

Figure

8 . 3 0 : Amplifier with linear optical AGC.

=

Signal output ;L,

8.8

393

Gain-flattening and clamping in fiber amplifiers

Signal

-10

i

I~ -20 0

:i

< reduced laser p o w e r

=

-4 0

o -50

-2dBm -30dBm

~

-30

Q.

.......

,,

-

power

,**J

1,...h,~

-6 0

1510

1520

1530

1540

1550

1560

1570

Wavelength / nm

Figure [134].

8.3 1: Output spectra of all-optical AGC amplifier, lasing at 1520 nm

the cavity loss at 2.5 dB, single pass. The pump power in the fiber from a 1480-nm diode laser was approximately 80 mW. Figure 8.31 shows the compensatory effect of the control laser in the broadband output spectra. As the input signal is increased to - 2 dBm from the small signal level ( - 3 0 dBm), there is more t h a n 10 dB of reduction in the residual laser output power. The inversion (and therefore the gain) in both cases remains the same. The excess noise in the high signal case is an artifact due to the side modes of the signal DFB source. The evolution of the amplifier gain at 1550 nm, as a function of input signal level for four different pump powers is shown in Fig 8.32. A gain of nearly 16 dB is m a i n t a i n e d up to an input signal power level of about - 5 dBm, at the m a x i m u m pump power level of 80 mW. The pump power no longer determines the amplifier's gain in the gain-controlled regime, only its m a x i m u m controlled output power. This is a desirable feature for a well-managed amplifier. The dynamic performance of amplifiers with and without gain control is compared in Figs. 8.33 and 8.34. To test the t r a n s i e n t response of the amplifiers an input signal o f - 10 dBm is modulated at 54 Hz and the outputs monitored on an oscilloscope, as shown in Fig. 8.33. Without the signal present, the population inversion builds up in the uncontrolled amplifier. When the signal is injected, the output overshoots,

394

Chapter 8

15

!!

llllI

Fiber Grating Lasers and Amplifiers

!! -

i

[=_I

Pump powers

"_

........

980mW

m 10 "o

52roW 933mW

A

c

923mW

.,,.,,

5

-40

-30

-20

-10

0

Input signal I dBm

F i g u r e 8.32: Gain characteristic of AGC amplifier. Lasing wavelength: 1520 nm; signal wavelength: 1550 nm; signal power: -30 dBm (from: Massicott J. F., Willson S. D., Wyatt R., Armitage J. R., Kashyap R., and Williams D., "1480nm pumped erbium doped fibre amplifier with all optical automatic gain control," Electron. Lett. 30(12), 962-963, 1994. 9 1994, Ref. [134]).

producing a spike before a new equilibrium is reached. In the optical gaincontrolled amplifier, the spike is eliminated. Additionally, the induced cross-talk is also eliminated, as shown in Fig. 8.34. A small counterdirectionally propagating probe at 1560 nm is strongly affected in the uncontrolled amplifier but remains unaffected with AGC. In the absence of AGC, the CW probe output power more than doubles when the saturating signal is blocked, whereas in the controlled case, a change of less t h a n 0.5% in output is seen. To eliminate the residual laser power at 1520 nm, an additional STG [122] with a rejection of 30 dB is used. BER measurements performed at 2.5 Gb/sec show no penalty as a result of operating the amplifier in the optical gain-controlled regime. A combination of both gain control and gain equalization forms a highly desirable amplifier. A GEQ filter composed of a concatenated set of STG filters, (as discussed in Section 8.8.1) added to the AGC amplifier output shows excellent GEQ-AGC. The flattened spectral shape is maintained for as long as the amplifier is operated within the gain-controlled range.

8.8

Gain-flattening and clamping in fiber amplifiers

---_

395

1

-

. m m

.d

Standard amplifier

AGC amplifier

o..

0

I

0

10

,

20

I,

Input , signal

I

40

30

50

Ti me / ms

Figure 8.33: 1550-nm input signal modulated at 54 Hz (bottom trace), signal amplified using gain control (middle trace), and signal amplified without gain control (top trace) (from: Massicott J. F., Wilson S. D., Wyatt R., Armitage J. R., Kashyap R., and Williams D., "1480nm pumped erbium doped fibre amplifier with all optical automatic gain control," Electron. Lett. 30(12), 962-963, 1994. 9 1994, Ref. [134]).

8.8.3

Analysis of gain-controlled

amplifiers

For an amplifying fiber in which the Er 3+ ion population inversion profile is approximated to be constant across the fiber core, the wavelengthdependent gain coefficient is given by g(z) = F(A)N[(ere(A ) + O-a(A))n 2

--

O'a(A)]

,

(8.8.1)

where ~e(Z) and ~ra(z) are the emission and absorption cross-sections, respectively, N is the axial Er 3§ ion density, n2 is the fraction of ions in the excited state, and F(z) is the confinement factor representing the overlap between the propagating mode and the radial ion density distribution. In an amplifier in which gain control is in operation, the population inversion, and hence n2, is set by the lasing condition, and amplifier gain calculations can be made without reference to the magnitudes of pump and signal power levels. The total linear loss at the laser cavity wavelength is Cavity loss

=

e 2g(Zas)L.

(8.8.2)

396

Chapter 8

Fiber Grating Lasers and Amplifiers

2.5 9 2.0 ,-

.E

,==: :'.'-'- --~:-~:-:.-........

f

t

_ .,~L.

no AGC

i

il

~- 1.5 -

e

! !

!

0

|

i

I

1~ e~l.

L.

~. . . . . .

with AGC

O 0.5 0.0 0

10

20

30

Ti m e / ms

40

50

8 . 3 4 : Cross-talk experienced by a contradirectionally propagating small signal 1560-nm probe to a modulated 1550-nm signal. Probe amplified using gain control (solid) and without gain control (dashed) [134].

Figure

Determination of the minimum required pump power to maintain gain control in the presence of signals of known magnitude is more involved. Approximate amplifier analyses (e.g., [135]) can be employed, but values so obtained substantially underestimate the actual power requirements. Principally, this is because no account is taken of pair induced quenching effects t h a t degrade power conversion efficiencies even in low Er 3+ ion concentration fibers [136].

8.8.4

Cavity

stability

The gain stability of the amplifier is determined by the stability of the control laser wavelength and the laser cavity loss. The laser wavelength is fixed by the narrow-linewidth grating reflectors that have a temperature sensitivity o f - 0 . 0 1 nm/~ To avoid changes in cavity loss if drifting should occur, the use of one narrow- and one broader-band reflector is preferable. Reflections at the laser wavelength from other parts of the transmission system will alter the effective cavity loss, as will polarization dependence combined with birefringence in the fiber. The use of highreflection gratings with an associated intracavity side-tap attenuator, as

8.8

397

Gain-flattening and clamping in f i b e r amplifiers

opposed to reflectors of lower reflectivity, offers greater resilience to stray light from other parts of the transmission system.

8.8.5

Noise

figure

The signal-spontaneous beat-noise figure for an amplifier is often given as

P~(~)

(8.8.3)

F(.) = h~,~d.G(~.) - 1)'

where P~(P) is the spontaneous emission power at frequency 9, measured in a bandwidth t~v. Over a length of fiber in which the population inversion is constant, the noise figure for t h a t inversion can be calculated using

(:re(A) n

"

(8.8.4)

It can be seen that for a given wavelength, the best noise figure is obtained for the highest possible inversion i.e., m a x i m u m n2/n 1. In a full-length amplifier, whether or not it is gain controlled, the local population inversion varies along the fiber length. The overall noise figure of the amplifier is predominantly determined at the signal input end [137], as spontaneous emission generated at the input experiences the full amplifier gain before being detected within the bandwidth of the signal receiver. In an AGC amplifier, the evolution of the population inversion is, in part, determined by the laser power. For good overall noise performance, it is beneficial to minimize the laser power at the input in order to ensure that, as far as possible, the input inversion is determined by the shorterwavelength pump source. This involves implementing as asymmetric a cavity configuration as possible. This is achieved by locating the bulk of the cavity loss at the signal output end of the amplifier and by choosing the wavelength of the control laser to be in a high-gain region of the spectrum requiring a correspondingly high cavity loss. Figure 8.35 shows the measured gain and noise figures of an AGC amplifier with a linear control laser cavity at 1530 nm [138]. The pump and signal powers are referenced to the input a n d output of the doped fiber and the measured noise figures are compared with data obtained using a full numerical amplifier model [139]. In one case the cavity loss

398

Chapter 8 Fiber Grating Lasers and Amplifiers 25

= gain A F front loss

2O

9 F back loss

m . m

"O

F modeleid 15 Laser: 1530nm 10-

Pump: 1480nm 65mW

I,I. k............ 9 ...................

Length:20m 0 1540

1545

1550

1555

1560

1565

1570

Wavelength I nm

F i g u r e 8 . 3 5 : Gain and noise figure for an AGC amplifier in two cavity implementations (courtesy J. Massicott, BT Laboratories).

g r a t i n g is placed at the front end of the cavity, and in the other, at the back. The gain spectra for the two cases were identical to w l~hin experim e n t a l error, b u t the expected noise figure i m p r o v e m e n t is achieved when the cavity loss is located at the signal o u t p u t end of the laser cavity.

References 1 Betti S., De Marchais G., and Iannone E., Coherent Optical Communications System, Wiley, New York (1995). 2 Olsson A. and Tang C. L., "Coherent optical interference effects in external cavity semiconductor lasers," IEEE J. Quantum Electron. QE-17, 1320-1323 (1981). 3 Tkach R. W. and Chraplyvy A. R., "Regimes of feedback effects in 1.5 t~m distributed feedback laser," J. Lightwave Technol. LT-4, 1655-1661 (1986). 4 Wyatt R. and Devlin W. J., "10kHz linewidth 1.5 ttm, InGaAsP external cavity laser with 55nm tuning range," Electron. Lett. 19, 110-112 (1983). 5 0 l s s o n N. A., Henry C. H., Kazarinov R. F., Lee H. J., and Orlowsky K. J., "Performance characteristics of a 1.5 ttm single frequency semiconductor

References

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400

Chapter 8 Fiber Grating Lasers and Amplifiers

18 Morton P. A., Mizrahi V., Tanbun-Ek, Logan R. A., Lemaire P. J., and Presby, H. M., "Stable single mode hybrid laser with high power and narrow linewidth," Appl. Phys. Lett. 64, 2634-2636 (1994). 19 Edwards C. A., Presby H. M., and Stulz L. W., "Effective reflectivity of hyperbolic micro lenses," Appl. Opt 32, 2099 (1993). 20 Giles C. R., Erdogan T., and Mizrahi V., "Simultaneous wavelength stabilisation of 980nm pump lasers," IEEE Photon. Technol. Lett. 6, 907-909 (1994). 21 Ventrudo B. F., Rogers G. A., Lick G. S., Hargreaves D., and Demayo T. N., "Wavelength and intensity stabilisation of 980nm diode lasers coupled to fiber Bragg gratings," Electron. Lett. 30(25), 2147-2149 (1994). 22 Petermann K., in Laser Diode Modulation and Noise," Chapter 7. Kluwer Academic Publishers, Dordrecht (1991). 23 Pan J. J., Jing X. L., and Shi Y., "Fiber grating stabilized source for dense WDM systems," in Proc. of Optical Fiber Conf., 0FC'97, paper WL48, p. 213. 24 Campbell R. J., Armitage J. R., Sherlock G., Williams D. L., Smith R. P., Robertson M. J., and Wyatt R., "Wavelength stable uncooled fiber grating semiconductor laser for use in an all optical WDM access network," Electron. Lett. 32, 119-120 (1996). 25 Collins J. V., Lealman I. F., Fiddyment P. J., Jones C. A., Waller R. G., Rivers L. J., Cooper K., Perrin S. D., Neild M. W., and Harlow M. J., "Passive alignment of a tapered laser with more than 50% coupling efficiency," Electron Lett. 31(9), 730-731 (1995). 26 Kashyap R., Payne R., Whitley T., and Sherlock G., "Wavelength uncommitted lasers," Electron. Lett. 30(13), 1065 (1994). 27 Timofeev F. N., Bayvel P., Midwinter J. E., Wyatt R., Kashyap R., and Robertson M., "2.5Gbit/s dense WDM, transmission in standard fibre using directly modulated fibre grating lasers," Electron Lett. 33(19), 1632-1633 (1997). 28 Timofeev F. N., Bayvel P., Mikhailov V., Gambini P., Wyatt R., Kashyap R., Robertson M., Campbell R. J., and Midwinter J. E., "Low chirp, 2.5 Gbit/s directly modulated fibre grating laser for WDM networks," in Technical Digest of Conf. on Opt. Fib. Commun., 0FC'97, p. 296 (1997). 29 Timofeev F. N., Bayvel P., Midwinter J. E., Wyatt R., Kashyap R., and Robertson M., "2.6 Gbit/s dense WDM transmission in standard fibre using directly modulated fibre grating lasers," Electron Lett. 33(19), 1632-1633 (1997). 30 Timofeev F. N., Bayvel P., Mikhailov V., Lavrova O. A., Wyatt R., Kashyap R., Robertson M., and Midwinter J. E., "2.5 Gbit/s directly modulated fibre grating laser for WDM network," Electron. Lett. 33(16), 1406-1407 (1997). 31 Timofeev F. N., Bennett S., Griffin R., Bayvel P., Seeds A., Wyatt R., Kashyap R., and Robertson M., "High spectral purity millimetre-wave modulated opti-

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402

Chapter 8 Fiber Grating Lasers and Amplifiers

44 Obro M., Pedersen J. E., and Brierley M. C., "Gain enhancement in Nd 3+ doped ZBLAN fibre amplifier using mode coupling filter," Electron. Lett. 28(1), 99-100 (1992). 45 Miller I. D. and Hunt M. H., "Optical fibre locating apparatus ," UK Patent no. 89301940, 27 February 1989. 46 Jauncey I. M., Reekie L., Mears R. J., Payne D. N., Rowe C. J., Reid D. C. J., Bennion L., and Edge C., "Narrow-linewidth fiber laser with integral fiber grating," Electron. Lett. 22(19), 987-988 (1986). 47 Wyatt R., "High power broadly tunable erbium-doped silica fiber laser," Electron. Lett. 25(22), 1498-1499 (1989). 48 Kashyap R., Armitage J. R., Wyatt R., Davey S. T., and Williams D. L., "Allfiber narrowband reflection gratings at 1500 nm, Electron. Lett. 26(11), 730 (1990). 49 Ball G. A., Morey W. W., and Waters J. P., "Nd 3+ fiber laser utilising intracore Bragg reflectors," Electron Lett 26(21), 1829 (1990). 50 Mizrahi V., DiGiovanni D., Atkins R. M., Park Y., and Delavaux J-MP "Stable single-mode erbium fiber grating laser for digital communication," IEEE J. Lightwave Technol. 11(12), 2021 (1993). 51 Zyskind J. L., Mizrahi V., DiGiovanni D. J., and Sulhoff J. W., "Short singlefrequency Erbium-doped fiber laser," Electron. Lett. 28, 1385 (1992). 52 Chernikov S. V., Kashyap R., McKee P. F., and Taylor J. R., "Dual frequency all fiber grating laser source," Electron Lett. 29(12), 1089 (1993). 53 Chernikov S. V., Taylor J. R., and Kashyap R., "Coupled-cavity erbium fiber lasers incorporating fiber grating reflectors," Opt. Lett. 18(23), 2023, 1993, and Chernikov S. V., Taylor J. R., and Kashyap R., "Integrated all optical fiber source ofmultigigahertz soliton pulse train," Electron. Lett. 29(20), 1788 (1993). 54 Ball G. A., Morey W. W., and Cheo P. K., "Single- and multipoint fiber-laser sensors," IEEE Photonics Tech. Lett. 5(2), 267 (1993). 55 Ball G. A. and Morey W. W., "Narrow-linewidth fiber laser with integrated master oscillator-power amplifier," Proc. Conference on Optical Fiber Communications, 0FC'92, p. 97 (1992). 56 Archambault J. L. and Grubb S. G., "Fiber gratings in lasers and amplifiers," J. Lightwave Technol. 15(8), 1378-1390 (1987). 57 Loh W. H., Laming R. I., and Zervas M. N., "Single frequency erbium fiber external cavity semiconductor laser," Appl. Phys. Lett. 66(25), 3422-3424 (1995). 58 Grubb S. G., "High power fiber amplifiers and lasers" in Proc. of 0FC'95, Tutorial Session (1996).

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59 SDL FL-10, SDL Inc., 80 Rose Orchard Way, San Jose, CA. USA. 60 Digonnet M. J. F., "Closed-form expressions for the gain in three- and fourlevel laser fibers," IEEE J. Quantum Electron. 26, 1788-1796 (1990). 61 Ball G. A. and Glenn W. H., "Design of a single-mode linear-cavity erbium fiber laser utilising Bragg reflectors," J. Lightwave Technol. 10(10), 1338 (1992). 62 Ball G. A., Glenn W. H., Morey W. W., and Cheo P. K., "Modelling of short, single-frequency, fiber lasers in high-gain fiber," IEEE Photonics Tech. Lett. 5(6), 649 (1993). 63 Le Boudec P., Francois P. L., Delevaque E., Bayon J.-F., Sanchez E., and Stephan G. M., "Influence of ion pairs on the dynamical behaviour of Er 3+ doped fiber lasers," Opt. & Quantum. Electron: 25, 501 (1993). 64 Ball G. A., Hul-Allen G., Holton C. E., and Morey W. W., "Low noise single frequency linear fibre laser," Electron. Lett. 29, 1623-1625 (1993). 65 Kane T. J., "Intensity noise in diode-pumped single-frequency Nd:YAG lasers and its control by electronic feedback," IEEE Photon. Technol. Lett. 2(4), 244- 245 (1990). 66 Zyskind J. L., Sulhoff J. W., Magill P. D., Reichmann K. C., Mizrahi V., and DiGiovanni D. J., "Transmission at 2.5 Gbit/s over 654 km using an erbiumdoped fiber grating laser source," Electron. Lett. 29(12), 1105 (1993). 67 Delavaux J.-M. P., Park Y. Y., Mizrahi V., and DiGiovanni D. J., "Long term bit error rate transmission using an erbium fiber grating laser transmitter at 5 and 2.5 Gb/s," in Tech. Proc. of ECOC'93, paper TuC3.3, pp. 69-71 (1993). 68 Ball G. A., Hul-Allen G., Holton C. E., and Morey W. W., "60 mW 1.5 /~m single-frequency low noise fibre laser MOPA," IEEE Photon. Technol. Lett. 6(2), 192-194 (1994). 69 Kringlebotn J. T., Archambault J. L., Reekie L., Townsend J. E., and Payne D. N., "Highly-efficient, low-noise grating-feedback Er+3:yb 3+ codoped fibre laser," Electron. Lett. 30(12), 972-973 (1994). 70 Kringlebotn J. T., Morkel P. R., Reekie L., Archambault J. L., and Payne D.N., "Efficient diode-pumped single frequency erbium:ytterbium fibre laser," IEEE Photonics Technol. Lett. 5(10), 1162 (1993). 71 Allain J. Y., Bayon J.-F,, and Monerie M., "Ytterbium-doped silica fiber laser with intracore Bragg gratings at 1.02/~m," Electron. Lett. 29, 309 (1993). 72 Coldren L. A., Millar B. I., Iga K., and Rentschler J. A., "Monolithic twosection GaInsAsP/InP active optical resonator devices formed by reactive ion etching," Appl. Phys. Lett. 38, 315 (1981).

404

Chapter 8 Fiber Grating Lasers and Amplifiers

73 Tsang W. T., Olsson N. A., and Logan R. A., "High speed direct single-frequency modulation with large tuning rate and frequency excursion in cleaved coupled cavity semiconductor laser," Appl. Phys. Lett. 42, 650 (1983). 74 Lang R. J., Yariv A., and Salzman J., "Laterally coupled cavities semiconductor lasers," IEEE J. Quantum Electron. QE-23, 395 (1987). 75 Dianov E. M. and Okhotnikov O. G., Sov. Lightwave Commun. 2, 823 (1992). 76 Pan J. J. and Shi Y., "Tunable Er +3-doped fibre ring laser using fibre grating incorporated by optical circulator or fibre coupler," Electron. Lett. 31(14), 1164-1165 (1995). 77 Guy M. J., Taylor J. R., and Kashyap R., "Single-frequency erbium fibre ring laser with intracavity phase-shifted fibre Bragg grating narrowband filter," Electron. Lett. 31(22), 1924-1925 (1995). 78 Yun S. H., Richardson D. J., Culverhouse D. O., and Kim B. Y., 'Wavelengthswept fiber laser with frequency-shifted feedback," in Tech. Digest of 0FC'97, pp. 30-31 (1997). 79 Dong L., Loh W. H., Caplen J. E., Hsu K., Minelli J. D., and Reekie L., "Photosensitive Er/Yb optical fibers for efficient single-frequency fiber lasers," in Tech. Digest of 0FC'97, pp. 29-30 (1997). 80 Dong L., Loh W. H., Caplen J. E., Hsu K., Minelli J. D., and Reekie L., "Efficient single-frequency fiber lasers with novel photosensitive Er/Yb optical fibers," Opt. Lett. 22(10), 694-696 (1997). 81 Utaka K., Akiba S., and Matsushima Y., "M4-shifted GaAsP/InP DFB lasers by simultaneous holographic exposure of negative and positive photoresists," Electron. Lett. 20, 1008-1010 (1984). 82 Asseh H., Storoy H., Kringlebotn J. T., Margulis W., Sahlgren B., and Sandgren S., "10 cm long Yb + DFB fibre laser with permanent phase shifted grating," Electron. Lett. 31, 969-970 (1995). 83 Sejka M., Varming P., Haiibner J., and Kristensen M., "Distributed feedback Er +3 doped fibre laser," Electron. Lett. 31(17), 1445-1446 (1995). 84 Loh W. H. and Laming R. I., "1.55 ~m phase-shifted distribute feedback fibre laser," Electron. Lett. 31(17), 1440-1442 (1995). 85 Hiibner J., Varming P., and Kristensen M. "Five wavelength DFB fibre laser source for WDM systems," Electron. Lett. 33(2), 139-140 (1997). 86 Lauridsen V. C., Sondergaard T., Varming P., and Povlsen J. H., "Design of distributed feedback fiber lasers," In Proc. of ECOC'97, Vol. 3, pp. 39-42 (1997). 87 Graydon O., Loh W. H., Laming R. I., and Dong L., "Triple-frequency operation of an Er-doped twin-core fiber loop laser," IEEE Photon. Technol. Lett. 8( 1 ), 63-65 (1996).

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88 Ball G. A. and Morey W. W., "Continuously tuneable single-mode erbium fiber laser," Opt. Lett. 17(6), 420 (1992). 89 Ball G.A. and Morey W.W., "Compression-tuned single-frequency Bragg grating fiber laser," Opt. Lett. 19(23), 1979-1981 (1994). 90 Hsu K., Loh W. H., Dong L., and Miller C. M., "Efficient and tunable Er/Yb fiber grating lasers," J, Lightwave Technol. 15(8), 1438-1441 (1997). 91 Gunning P., Kashyap R., Siddiqui A. S., and Smith K., "Picosecond pulse generation of

-0.5

r m

=

.' /

.7-..-

.......... ::;

-0.25

rr-

-0 0

1000

2000 3000 K:(per rn)

4000

5000

Figure 9 . 3 : The reflectivity and bandwidth of three Bragg gratings as a function of the coupling constant Kac at a wavelength of 1550 nm. The numbers refer to the lengths in millimeters. Note that for large values of the coupling constant, the grating bandwidth grows linearly. As a guide, the maximum refractive index modulation amplitude, An, for v = 1, and overlap, y = 0.8, is ---3 • 10 -3 (at Kac = 5000 m-l).

9.1

Measurement of reflection and transmission spectra of Bragg gratings

413

where we remind ourselves t h a t An is the ac index change and A is the Bragg wavelength at the start of the growth of the grating. As the grating grows, it shifts to longer wavelengths and this is shown in the transmission spectra in Fig. 9.4. Along with the shift is shown the effect of a nonuniform UV beam profile. This has been assumed to have a Gaussian profile, as with m a n y laser beams, and causes a chirp in the grating [1], since the Bragg wavelength is proportional to the effective mode index. There are two effects of the nonuniform UV beam profile: The grating acquires additional structure on the short-wavelength side (Fig. 9.4) as it grows, and the peak reflectivity drops for the same refractive index modulation amplitude, as is seen for the uniform profile grating in Fig. 9.5. Comparing the uniform and the Gaussian intensity profile grating, the effect on the bandwidth is only slight. The long-wavelength edge of the Gaussian profile grating is apodized. We now compare the Gaussian intensity profile with the Gaussian apodized grating, i.e., one in which the refractive index modulation changes with the length of the grating, but not the mode effective index (see Chapter 5), and find t h a t the short-wavelength s t r u c t u r e disappears and the peak reflectivity increases with apodization. The reason for this is t h a t the Bragg wavelength of the apodized grating is constant and the

1551

1552

1553

1554

1555

1556

0 ca-10

E

o -20 t~

'.,k\ .,.~.-" ~ -

f B

i /

/

/o

-

..,=..

E -30

-

t'-

"-

-4

0

-

.....

. . . . .

an = 1 e - 3 (B)

....... dn = e e - 3 ( C ) -50

Wavelength, nm

F i g u r e 9.4: The shift in the Bragg wavelength and the appearance of the Fabry-Perot structure on the short-wavelength side ofa Gaussian intensity profile grating as the UV-induced refractive index modulation amplitude increases.

414

Chapter 9 1551 ~._

,,~

Measurement and Characterization of Gratings

1552 ..... ~-~. ~ ~ . ;~

1553

1555

1554 :, .,~,~-~, ' ~ . . . . . .

I

,___

,

m -10

g "~ ~ = "~

g ~-

':

eo

i

t |

30 40 5O 6O 70

k = 4ram dn =le-a(max)

, ~

~ '~;

/

",.,,

';''\\

/ ~.J /

Uniform

Wavelength, nm 9 . 5 : A uniform amplitude profile grating compared with a Gaussian amplitude profile grating.

Figure

reflection is not s p r e a d over a l a r g e r b a n d w i d t h , and so the effective l e n g t h is longer. (See Fig. 9.6.) The m a x i m u m reflectivity can be calculated by m e a s u r i n g the transmission dip T d in dBs. The t r a n s l a t i o n from the m e a s u r e d dip to the reflectivity is R = 1-

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~- -50.0

I

1555 fl

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Gaussian am pitude profile beam

-60.0 Wavelength, nm

F i g u r e 9 . 6 : Comparison of chirp induced in a strong grating due to the amplitude profile of the writing beam and a Gaussian profile apodized grating with the same parameters. The FWFZ bandwidth is approximately the same, but the slope on the long wavelength side is different, as well as the structure on the short wavelength side.

9.1

Measurement of reflection and transmission spectra of Bragg gratings

415

or from the peak of the reflected signal Rp below the t r a n s m i t t e d signal it is (as shown in Fig. 9.2) (9.1.6)

R = 10 -Rp/10.

The data is shown in Fig. 9.7. For example, in Fig. 9.2, the reflected signal is shown to be - 7 0 dB below the transmission level. This t r a n s l a t e s to a reflectivity of 10-5%. Alternatively, a 10-dB transmission dip is equivalent to a reflectivity of 90%, 20 dB is 99%, and so on. It is a s s u m e d t h a t there is no additional loss in the reflected signal as compared with the t r a n s m i t t e d signal. If the loss is known, the t r a n s m i t t e d level or the reflection peak m u s t be adjusted accordingly. Special care needs to be t a k e n when m e a s u r i n g transmission dips in excess o f - 3 0 dB because of the limited resolution of the spectrum analyzer. The slit width of the spectrum analyzer is not a delta function, and there is substantial leakage from the spectral region outside of the slit bandwidth. Integrated, it amounts to more signal being t r a n s m i t t e d and affects the spectrum mostly at the dip in the grating transmission. There are several solutions to this problem. Obviously, a better spectrum analyzer is one, or a tunable laser source m a y be used in conjunction with a conventional spectrum analyzer, ensuring t h a t the scanning of the laser and the spectrum analyzers are synchronized [2] with an appropriate slit width. The combined side-mode suppression and the slit width reduces

0.8

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0.20

5

10

15

20

25

30

T-dip or R-peak, dB

F i g u r e 9.7: Reflectivity as a function of the dip in the transmission spectrum of a grating or as the reflection peak below transmitted signal.

416

Chapter 9 Measurement and Characterization of Gratings

the captured noise. Such a m e a s u r e m e n t is shown in Fig. 9.8, in which the spectrum of a strong 4-mm-long grating spectrum with a transmission dip of >60 dB has been resolved. In addition to the very steep longwavelength edge, it has structure on the short wavelength that is due to cladding mode coupling and Gaussian chirp. Clearly, chirp is not a feature t h a t is desirable for simple transmission filters. We now consider the spectra of uniform period gratings and the effect of apodization. Figure 9.9 shows the reflection spectrum of unapod-

1.540

1.542

1.544

1.546

1.548

1.550

0

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-20

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-80 Wavelength, lam

F i g u r e 9.8: The measured grating is ~4 nm long with an estimated index modulation of 4 x 10 -3. The beam intensity profile had a Gaussian shape. The inset shows the change in the Bragg wavelength across the length of the grating.

F i g u r e 9.9: Reflection spectra of 4-mm-long unapodized and cos2 apodized gratings with a refractive index modulation amplitude of 4 x 10 -4.

9.2 Perfect Bragg gratings

417

ized and apodized (cos 2 profile) gratings. The unapodized grating is nominally a 100% reflection grating, and the apodized one has identical length and refractive index modulation. The effect of apodization is to reduce the effective length to approximately L/2. As a result, the FWFZ bandwidth approximately matches the second zeroes of the unapodized grating. Note that the reflectivity is also reduced (-halved). To generate an apodized grating with the same bandwidth, the length has to be approximately doubled, and the coupling constant has to be adjusted, so t h a t an 8mm-long raised cosine apodized grating will have the same approximate bandwidth and reflectivity. In order to resolve the reduced side lobes for the apodized grating, the spectrum analyzer linewidth should be selected to remove artifacts and a false noise floor.

9.2

Perfect Bragg gratings

It is possible to make very high-quality uniform-period Bragg gratings. This is because optical fiber has very uniform properties. The theoretically calculated reflection, along with the measured spectrum, of a 30-mm-long grating is shown in Fig. 9.10. The grating was fabricated by scanning a phase mask with a UV beam [3].

F i g u r e 9.10: Measured and computed reflection spectrum of a 29.5-mm-long fiber Bragg grating, produced by the scanned phase-mask technique [4]. The uniformity of the grating is indicated by the close agreement between the zeroes of the theoretical and measured response.

418

Chapter 9

Measurement and Characterization of Gratings

The agreement between m e a s u r e m e n t and theory is very good, with the zeroes matching across almost the entire spectrum shown. Notice the slight deviations, especially at the first side-lobe zero (RHS), and the third side-lobe zero (LHS). These features are indicative of slight chirp and nonuniformity in the writing process. Nevertheless, this grating has ~28,000 grating periods and shows a near-ideal response. One way to measure such a narrow bandwidth is to use a high-quality tunable laser source and a spectrum analyzer for reasons of resolution. It is difficult to measure such gratings accurately in transmission with a broadband source, since the bandwidth is almost the same as that of commercially available optical spectrum analyzers (0.07 nm FWHZ). Although this grating has a transmission dip of ~14 dB, the spectrum remains unresolved in transmission with a spectrum analyzer. Gratings with such performance are particularly useful where the phase response is required along with the reflection characteristics in filtering applications, such as in pulse shaping and dark soliton generation

[4].

9.3

Phase and temporal response gratings

of Bragg

Figure 9.11 shows the computed reflection and accumulated phase-spect r u m of a uniform-period unapodized Bragg grating. The measurement of phase of a grating can only be made by the m e a s u r e m e n t of the grating's complex amplitude reflectivity. A technique has been proposed for the reconstruction of the phase of the grating using arguments based on causality and m i n i m u m phase performed on the measured reflection spect r u m of a grating, with reasonable success [5]. This may be done by using interferometric techniques to characterize weak gratings (